Sesión 06

Diseño de experimentos en arreglo de parcelas

divididas y arreglos especiales


Christian Vásquez-Velasco, Bach., M.Sc.(c)

InkaStats Academy

2023

Instalar paquetes necesarios


# install.packages("devtools")
# devtools::install_github("emitanaka/edibble", force = T)
# devtools::install_github("emitanaka/deggust", force = T)

if (!require("pacman")) install.packages("pacman")
pacman::p_load(readxl, agricolae, agricolaeplotr, car, tidyverse, PMCMRplus, 
               outliers, nortest, mvtnorm, lmtest, ExpDes, edibble, gt,
               gtsummary, devtools, deggust, xlsx, desplot,
               ggResidpanel, fastGraph, gvlma, multcomp,
               phia, dvmisc)
package 'xlsx' successfully unpacked and MD5 sums checked

The downloaded binary packages are in
    C:\Users\cvasquezv\AppData\Local\Temp\Rtmpy0PSlr\downloaded_packages

Diseño completamente al azar en arreglo de parcelas divididas

Planeamiento


Crear un libro de campo con el paquete agricolae


trt1 <- c("Ventura","Biloxi","Emerald")
trt2 <- c("50 kg.ha N","100 kg.ha N")

r <- 5

salida <- agricolae::design.split(trt1 = trt1,
                                  trt2 = trt2,
                                  r = r,
                                  design = "crd",
                                  serie = 3,
                                  seed = 123,
                                  kinds = "Super-Duper",
                                  randomization = TRUE)
salida$book %>% 
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)

Guardar el libro generado

write.table(salida$book,
            "books/crdspsplit.txt",
            row.names = FALSE,
            sep = "\t")

write.xlsx(salida$book,
           "books/crdspsplit.xlsx",
           sheetName = "book",
           append = FALSE,
           row.names = FALSE)
agricolaeplotr::plot_split_crd(
  design = salida,
  factor_name_1 = "trt1",
  factor_name_2 = "trt2",
  labels = "plots",
  subplots = FALSE,
  ncols = 6,
  nrows = 5,
  reverse_y = TRUE) +
  labs(fill = "Variedades",
       x = "Columnas",
       y = "Filas")
agricolaeplotr::plot_split_crd(
  design = salida,
  factor_name_1 = "trt1",
  factor_name_2 = "trt2",
  labels = "plots",
  subplots = TRUE,
  ncols = 6,
  nrows = 5,
  reverse_y = TRUE) +
  labs(fill = "Dosis de Nitrógeno",
       x = "Columnas",
       y = "Filas")

Crear un libro de campo con el paquete edibble


menu_split()
design("Split-Plot Design | Split-Unit Design") %>%
  set_units(mainplot = 12,
             subplot = nested_in(mainplot, 5)) %>%
  set_trts(trt1 = 4,
           trt2 = 5) %>%
  allot_trts(trt1 ~ mainplot,
             trt2 ~ subplot) %>%
  assign_trts("random", seed = 411) %>%
  serve_table()
crd <- takeout(menu_split(t1 = 3,
                          t2 = 2,
                          r = 5,
                          seed = 123))
crd %>% 
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)
crd2 <- design("Split-Plot Design | Split-Unit Design") %>%
  set_units(mainplot = 15,
            subplot = nested_in(mainplot, 2)) %>%
  set_trts(trt1 = trt1,
           trt2 = trt2) %>%
  allot_trts(trt1 ~ mainplot,
             trt2 ~ subplot) %>%
  assign_trts("random", seed = 123) %>%
  serve_table()
crd2 %>% 
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)
deggust::autoplot(crd)
plot(crd2)

Análisis de DCA en arreglo de parcelas divididas


Importación de datos


archivos <- list.files(pattern = "datos split plot.xlsx", 
                       full.names = TRUE,
                       recursive = TRUE)

# Importación
data <- readxl::read_xlsx(archivos,
                           sheet = "dca")

# Preprocesamiento

data <- data %>%
  mutate_if(is.character, factor) %>%
  mutate(rep = factor(rep))

Creación del modelo lineal


modelo.dca1 <- lm(rdto ~ A * B + rep/A - rep, data = data)
modelo.dca2 <- lm(rdto ~ A * B + rep:A - rep, data = data)
modelo.dca3 <- lm(rdto ~ A + B + rep/A - rep, data = data)
modelo.dca4 <- lm(rdto ~ A + B + rep:A - rep, data = data)

Nota

  • La expresión “rep/A” es para considerar la interacción como efecto fijo.
  • La expresión “rep:A” es para considerar la interacción como efecto aleatorio.
broom::glance(modelo.dca1) %>%
  bind_rows(broom::glance(modelo.dca2),
            broom::glance(modelo.dca3),
            broom::glance(modelo.dca4)) %>%
  dplyr::mutate(Modelo = c("A * B + rep/A",
                           "A * B + rep:A",
                           "A + B + rep/A",
                           "A + B + rep:A")) %>%
  dplyr::select(Modelo, AIC, BIC) %>%
  dplyr::arrange(BIC) %>%
  dplyr::mutate(Mérito = 1:n()) %>%
  dplyr::relocate(Mérito, Modelo) %>%
  gt()
Mérito Modelo AIC BIC
1 A * B + rep/A 84.76335 94.55744
2 A * B + rep:A 84.76335 94.55744
3 A + B + rep/A 121.70347 129.71682
4 A + B + rep:A 121.70347 129.71682

Definición del modelo


modelo.dca <- lm(rdto ~ A * B + rep/A - rep, data = data)

\[Y_i = \beta_0 + \beta_1*A_2 + \beta_2*B_2 + \beta_3*B_3 + \beta_4*A_2*B_2 + \beta_5*A_2*B_3 + \beta_6*A_1*rep_2 + \beta_7*A_1*rep_3 + \beta_8*A_2*rep_2 + \beta_9*A_2*rep_3 + \epsilon_i\]

\[\hat{Y}_i = \beta_0 + \beta_1*A_2 + \beta_2*B_2 + \beta_3*B_3 + \beta_4*A_2*B_2 + \beta_5*A_2*B_3 + \beta_6*A_1*rep_2 + \beta_7*A_1*rep_3 + \beta_8*A_2*rep_2 + \beta_9*A_2*rep_3\]

summary(modelo.dca)

Call:
lm(formula = rdto ~ A * B + rep/A - rep, data = data)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.3333 -0.7778  0.1111  0.9167  3.0000 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept)   2.6667     1.5466   1.724  0.12296   
Aa2           1.7778     2.1872   0.813  0.43985   
Bb2          -1.6667     1.6942  -0.984  0.35406   
Bb3           7.6667     1.6942   4.525  0.00194 **
Aa2:Bb2       9.3333     2.3960   3.895  0.00457 **
Aa2:Bb3     -10.6667     2.3960  -4.452  0.00213 **
Aa1:rep2      1.3333     1.6942   0.787  0.45397   
Aa2:rep2      0.3333     1.6942   0.197  0.84893   
Aa1:rep3      1.6667     1.6942   0.984  0.35406   
Aa2:rep3     -0.6667     1.6942  -0.393  0.70423   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.075 on 8 degrees of freedom
Multiple R-squared:  0.9072,    Adjusted R-squared:  0.8028 
F-statistic: 8.688 on 9 and 8 DF,  p-value: 0.002851

Verificación visual de los supuestos del modelo


performance::check_model(modelo.dca)
ggResidpanel::resid_panel(modelo.dca)
influence.measures(modelo.dca)
Influence measures of
     lm(formula = rdto ~ A * B + rep/A - rep, data = data) :

      dfb.1_ dfb.Aa2   dfb.Bb2   dfb.Bb3 dfb.A2.B2 dfb.A2.B3  dfb.A1.2
1   1.07e+00 -0.7582 -5.87e-01 -5.87e-01  4.15e-01  4.15e-01 -5.87e-01
2   0.00e+00  0.0000  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
3  -4.29e-01  0.3033  4.89e-17 -5.87e-01 -1.04e-16  4.15e-01  5.87e-01
4  -1.21e-16  0.9063 -4.43e-16 -6.75e-17 -4.96e-01 -4.96e-01  2.04e-16
5  -1.34e-16 -0.5362  3.47e-16  1.75e-16 -7.34e-01 -3.12e-16 -7.37e-17
6   2.00e-17  0.1200 -7.22e-17 -6.70e-17  4.11e-17  1.64e-01  3.12e-17
7   3.13e-01 -0.2212 -4.28e-01 -4.28e-01  3.03e-01  3.03e-01  4.28e-01
8  -1.02e-01  0.0723  2.80e-01 -9.26e-17 -1.98e-01  1.56e-16  2.80e-01
9   2.79e-01 -0.1970  1.27e-16 -7.63e-01 -1.80e-16  5.39e-01 -7.63e-01
10  5.65e-17 -0.1697  7.05e-17  3.16e-17  2.32e-01  2.32e-01 -1.13e-16
11 -3.02e-17 -0.1813  1.06e-16  9.56e-17  4.96e-01 -1.55e-16  1.93e-17
12  3.53e-17  0.0849 -1.25e-16 -3.16e-17  1.55e-16 -2.32e-01 -2.51e-17
13 -8.79e-01  0.6216  1.20e+00  1.20e+00 -8.51e-01 -8.51e-01  1.42e-16
14  1.02e-01 -0.0723 -2.80e-01  7.77e-17  1.98e-01 -1.44e-16 -8.25e-17
15 -7.07e-01  0.4997 -1.61e-16  1.94e+00  4.56e-16 -1.37e+00  1.03e-15
16  2.83e-17 -0.1697  1.41e-16  6.32e-17  2.32e-01  2.32e-01 -7.63e-17
17  2.00e-17 -0.0600  1.21e-17  2.42e-17  1.64e-01 -3.03e-17 -1.98e-17
18  0.00e+00 -0.0238  1.92e-17  0.00e+00 -2.71e-17  6.52e-02 -3.34e-18
    dfb.A2.2  dfb.A1.3  dfb.A2.3     dffit   cov.r   cook.d   hat inf
1   1.53e-16 -5.87e-01  1.40e-16  1.07e+00 2.48880 1.16e-01 0.556   *
2   0.00e+00  0.00e+00  0.00e+00 -1.13e-15 8.55268 1.47e-31 0.556   *
3  -1.13e-16  5.87e-01 -7.55e-17 -1.07e+00 2.48880 1.16e-01 0.556    
4  -7.02e-01  1.67e-16 -7.02e-01  1.28e+00 1.53070 1.58e-01 0.556    
5   1.04e+00 -3.53e-17  1.04e+00 -1.90e+00 0.27401 2.91e-01 0.556   *
6  -2.32e-01  2.37e-17 -2.32e-01  4.24e-01 6.97667 2.02e-02 0.556   *
7  -1.19e-16 -2.48e-16 -7.19e-17  7.82e-01 4.35231 6.53e-02 0.556    
8   5.34e-17  1.24e-16  6.86e-17  5.11e-01 6.37016 2.90e-02 0.556   *
9  -1.87e-16 -1.82e-16 -1.31e-16 -1.39e+00 1.15490 1.81e-01 0.556    
10 -3.29e-01 -7.82e-17 -1.84e-17 -6.00e-01 5.71482 3.95e-02 0.556   *
11  7.02e-01 -7.16e-17  3.07e-17  1.28e+00 1.53070 1.58e-01 0.556    
12 -3.29e-01  1.12e-17  3.95e-18 -6.00e-01 5.71482 3.95e-02 0.556   *
13  3.30e-16 -1.20e+00  2.02e-16 -2.20e+00 0.10552 3.56e-01 0.556   *
14 -7.13e-17 -2.80e-01 -6.86e-17 -5.11e-01 6.37016 2.90e-02 0.556   *
15  2.37e-16  1.94e+00  6.98e-17  3.53e+00 0.00121 5.88e-01 0.556   *
16 -9.67e-17 -5.59e-17 -3.29e-01 -6.00e-01 5.71482 3.95e-02 0.556   *
17 -1.37e-17 -3.95e-17  2.32e-01  4.24e-01 6.97667 2.02e-02 0.556   *
18 -3.26e-17 -9.40e-18  9.22e-02  1.68e-01 8.28075 3.23e-03 0.556   *
influenceIndexPlot(modelo.dca)

Cumplimiento de supuestos del modelo lineal general


Independencia de residuos

\(H_0: \text{Los residuos del rendimiento son completamente aleatorios e independientes}\)

\(H_1: \text{Los residuos del rendimiento no son completamente aleatorios e independientes}\)

durbinWatsonTest(modelo.dca,
                 reps = 5000,
                 max.lag = 5)
 lag Autocorrelation D-W Statistic p-value
   1     -0.25591398      2.458781  0.8248
   2     -0.35161290      2.641219  0.3708
   3      0.07741935      1.713978  0.9276
   4      0.26845878      1.000358  0.4244
   5     -0.17275986      1.740502  0.2448
 Alternative hypothesis: rho[lag] != 0
dwtest(modelo.dca, alternative = "two.sided")

    Durbin-Watson test

data:  modelo.dca
DW = 2.4588, p-value = 0.8145
alternative hypothesis: true autocorrelation is not 0

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los residuos del rendimiento son completamente aleatorios e independientes.

Normalidad de residuos

\(H_0: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

\(H_1: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

shapiro.test(rstudent(modelo.dca))

    Shapiro-Wilk normality test

data:  rstudent(modelo.dca)
W = 0.95347, p-value = 0.482
ad.test(rstudent(modelo.dca))

    Anderson-Darling normality test

data:  rstudent(modelo.dca)
A = 0.28753, p-value = 0.5783
lillie.test(rstudent(modelo.dca))

    Lilliefors (Kolmogorov-Smirnov) normality test

data:  rstudent(modelo.dca)
D = 0.12222, p-value = 0.6786
ks.test(rstudent(modelo.dca), "pnorm",
        alternative = "two.sided")

    Exact one-sample Kolmogorov-Smirnov test

data:  rstudent(modelo.dca)
D = 0.12079, p-value = 0.9274
alternative hypothesis: two-sided
cvm.test(rstudent(modelo.dca))

    Cramer-von Mises normality test

data:  rstudent(modelo.dca)
W = 0.035902, p-value = 0.7384
pearson.test(rstudent(modelo.dca))

    Pearson chi-square normality test

data:  rstudent(modelo.dca)
P = 3, p-value = 0.5578
sf.test(rstudent(modelo.dca))

    Shapiro-Francia normality test

data:  rstudent(modelo.dca)
W = 0.94303, p-value = 0.2775

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la distribución de los residuos del rendimiento es similar a la función normal o gaussiana.

Homocedasticidad

\(H_0\): La varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento

\(H_1\): La varianza del rendimiento no es constante con respecto a los valores ajustados del rendimiento

ncvTest(modelo.dca)
Non-constant Variance Score Test 
Variance formula: ~ fitted.values 
Chisquare = 4.009865, Df = 1, p = 0.045235
bptest(modelo.dca)

    studentized Breusch-Pagan test

data:  modelo.dca
BP = 14.223, df = 9, p-value = 0.1146
bptest(modelo.dca, studentize = F)

    Breusch-Pagan test

data:  modelo.dca
BP = 10.037, df = 9, p-value = 0.3475
olsrr::ols_test_breusch_pagan(modelo.dca)

 Breusch Pagan Test for Heteroskedasticity
 -----------------------------------------
 Ho: the variance is constant            
 Ha: the variance is not constant        

              Data               
 --------------------------------
 Response : rdto 
 Variables: fitted values of rdto 

        Test Summary          
 -----------------------------
 DF            =    1 
 Chi2          =    4.009865 
 Prob > Chi2   =    0.04523478 

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento.

Recomendación. Debido a que se cumple con el supuesto de homocedasticidad, para evaluar los efectos de los tratamientos con respecto al rendimiento, se debe proceder a realizar el análisis de varianza.

Estadísticas globales

modelo.dca %>% gvlma()

Call:
lm(formula = rdto ~ A * B + rep/A - rep, data = data)

Coefficients:
(Intercept)          Aa2          Bb2          Bb3      Aa2:Bb2      Aa2:Bb3  
     2.6667       1.7778      -1.6667       7.6667       9.3333     -10.6667  
   Aa1:rep2     Aa2:rep2     Aa1:rep3     Aa2:rep3  
     1.3333       0.3333       1.6667      -0.6667  


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = .) 

                     Value p-value                Decision
Global Stat        3.20107  0.5248 Assumptions acceptable.
Skewness           0.07893  0.7788 Assumptions acceptable.
Kurtosis           0.25987  0.6102 Assumptions acceptable.
Link Function      2.78083  0.0954 Assumptions acceptable.
Heteroscedasticity 0.08145  0.7753 Assumptions acceptable.

Análisis de varianza

\[Y_{ijk} = \mu + \tau_{i} + \text{Error}(\tau\text{rep})_{ik} + \beta_{j} + (\tau\beta)_{ij} + \epsilon_{ijk}\]

\[\hat{Y}_{ijk} = \mu + \tau_{i} + \text{Error}(\tau\text{rep})_{ik} + \beta_{j} + (\tau\beta)_{ij}\]

Dónde:

\(Y_{ijk}\) = Valor observado de la variable respuesta.

\(\hat{Y}_{ijk}\) = Valor ajustado de la variable respuesta.

\(\mu\) = Promedio observado de la variable respuesta.

\(\tau_{i}\) = Efecto del i-ésimo nivel del factor A.

\(\text{Error}(\tau\text{rep})_{ik}\) = Residuo observado del modelo a nivel de parcelas principales.

\(\beta_{j}\) = Efecto del j-ésimo nivel del factor B.

\((\tau\beta)_{ij}\) = Efecto de interacción del factor A x factor B dentro de los niveles ij.

\(\epsilon_{ijk}\) = Residuo observado del modelo a nivel de subparcelas.

Pruebas de hipótesis

Para el factor A (Variedad):

\(H_0: \tau_{A1} = \tau_{A2} = 0\)

\(H_1: \text{En al menos un nivel del factor A el } \tau \text{ es diferente a los demás.}\)

\(H_1: \tau_i \neq 0\text{; en al menos un nivel del factor A.}\)

Para el factor B (Densidad):

\(H_0: \beta_{B1} = \beta_{B2} = \beta_{B3} = 0\)

\(H_1: \text{En al menos un nivel del factor B el } \beta \text{ es diferente a los demás.}\)

\(H_1: \beta_j \neq 0\text{; en al menos un nivel del factor B.}\)

Para la interacción entre factor A y factor B:

\(H_0: (\tau\beta)_{A1B1} = (\tau\beta)_{A1B2} = (\tau\beta)_{A1B3} = (\tau\beta)_{A2B1} = (\tau\beta)_{A2B2} = (\tau\beta)_{A2B3} = 0\)

\(H_1: \text{En al menos una interacción entre el factor A y el factor B el } (\tau\beta) \text{ es diferente a los demás.}\)

\(H_1: (\tau\beta)_{ij} \neq 0\text{; en al menos una interacción entre el factor A y el factor B.}\)

Precaución

  • Si se ignora el diseño experimental, se obtienen los siguientes resultados, incorrectos. Observe que los grados de libertad del error es mayor, lo que facilita la detección de diferencias que en realidad no existen.
anova(modelo.dca, test = "F")
Analysis of Variance Table

Response: rdto
          Df  Sum Sq Mean Sq F value    Pr(>F)    
A          1   0.222   0.222  0.0516 0.8259782    
B          2  29.778  14.889  3.4581 0.0827438 .  
A:B        2 300.444 150.222 34.8903 0.0001119 ***
A:rep      4   6.222   1.556  0.3613 0.8296470    
Residuals  8  34.444   4.306                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Importante

Necesitamos especificar correctamente el término de error para el factor A. Debe tenerse en cuenta que la forma del Error es “Error(A:parcelagrande)” en el caso de efectos aleatorios o “Error(A:rep)” para el caso de efectos fijos y puede cambiar dependiendo de la disposición de los datos. La clave es conocer los grados de libertad correcto para saber que se obtienen los resultados correctos.

aov(rdto ~ A * B + Error(rep/A), data = data) -> aov.dca
summary(aov.dca)

Error: rep
          Df Sum Sq Mean Sq F value Pr(>F)
Residuals  2  2.111   1.056               

Error: rep:A
          Df Sum Sq Mean Sq F value Pr(>F)
A          1  0.222  0.2222   0.108  0.774
Residuals  2  4.111  2.0556               

Error: Within
          Df Sum Sq Mean Sq F value   Pr(>F)    
B          2  29.78   14.89   3.458 0.082744 .  
A:B        2 300.44  150.22  34.890 0.000112 ***
Residuals  8  34.44    4.31                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
broom::tidy(aov.dca)
# A tibble: 6 × 7
  stratum term         df   sumsq  meansq statistic   p.value
  <chr>   <chr>     <dbl>   <dbl>   <dbl>     <dbl>     <dbl>
1 rep     Residuals     2   2.11    1.06     NA     NA       
2 rep:A   A             1   0.222   0.222     0.108  0.774   
3 rep:A   Residuals     2   4.11    2.06     NA     NA       
4 Within  B             2  29.8    14.9       3.46   0.0827  
5 Within  A:B           2 300.    150.       34.9    0.000112
6 Within  Residuals     8  34.4     4.31     NA     NA       

Valor de la tabla de F para el factor A con una significancia de 0.05.

qf(0.95, 1, 2)
[1] 18.51282

Valor de la tabla de F para el factor B con una significancia de 0.05.

qf(0.95, 2, 8)
[1] 4.45897

Valor de la tabla de F para la interacción A:B con una significancia de 0.05.

qf(0.95, 2, 8)
[1] 4.45897
shadeDist(qf(0.95, 2, 8), "df",2, 8, lower.tail = F)

Conclusión.

Con respecto al Factor A: A un nivel de significancia de 0.05, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los niveles del factor A tienen un efecto sobre el rendimiento estadísticamente similar a 0.

Con respecto al Factor B: A un nivel de significancia de 0.05, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los niveles del factor B tienen un efecto sobre el rendimiento estadísticamente similar a 0.

Con respecto a la interacción entre el Factor A y Factor B: A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos una interacción entre un nivel del factor A y un nivel del factor B existe un efecto de antagonismo o sinergismo sobre el rendimiento.

agricolae::cv.model(modelo.dca)
[1] 35.91317

Comparaciones de medias para los efectos principales del Factor A

get_df_ea_spplot <- function(object) {
  library(broom)
  tidy_aov <- broom::tidy(object)
  df_rep_A_residuals <- tidy_aov %>% 
    dplyr::filter(grepl(":", stratum) & 
                    term == "Residuals") %>%
    dplyr::pull(df)
  return(df_rep_A_residuals)
}
get_df_ea_spplot(aov.dca)
[1] 2
get_mse_ea_spplot <- function(object) {
  library(broom)
  tidy_aov <- broom::tidy(object)
  meansq_rep_A_residuals <- tidy_aov %>% 
    dplyr::filter(grepl(":", stratum) & 
                    term == "Residuals") %>%
    dplyr::pull(meansq)
  return(meansq_rep_A_residuals)
}
get_mse_ea_spplot(aov.dca)
[1] 2.055556
data %>% with(LSD.test(
  rdto, # Cambiar según nombre de variable respuesta
  A, # Cambiar según nombre de variable independiente
  DFerror = get_df_ea_spplot(aov.dca), 
  MSerror = get_mse_ea_spplot(aov.dca),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: rdto ~ A

LSD t Test for rdto 

Mean Square Error:  2.055556 

A,  means and individual ( 95 %) CI

       rdto      std r      LCL      UCL Min Max
a1 5.666667 4.690416 9 3.610399 7.722934   1  15
a2 5.888889 4.935698 9 3.832621 7.945157   1  14

Alpha: 0.05 ; DF Error: 2
Critical Value of t: 4.302653 

least Significant Difference: 2.908002 

Treatments with the same letter are not significantly different.

       rdto groups
a2 5.888889      a
a1 5.666667      a

Comparaciones de medias para las interacciones

Para los niveles del factor A dentro del nivel B1:

  • A1 vs A2:

\(H_0: \mu_{A1} - \mu_{A2} = 0\)

\(H_1: \mu_{A1} - \mu_{A2} \neq 0\)

Para los niveles del factor B dentro del nivel A1:

  • B1 vs B2:

\(H_0: \mu_{B1} - \mu_{B2} = 0\)

\(H_1: \mu_{B1} - \mu_{B2} \neq 0\)

  • B1 vs B3:

\(H_0: \mu_{B1} - \mu_{B3} = 0\)

\(H_1: \mu_{B1} - \mu_{B3} \neq 0\)

  • B2 vs B3:

\(H_0: \mu_{B2} - \mu_{B3} = 0\)

\(H_1: \mu_{B2} - \mu_{B3} \neq 0\)

NOTA: Repetir este proceso para cada nivel de A y cada nivel de B.

Análisis de varianza para interacción de dos factores con el paquete phia

Comparación de los niveles de B dentro de cada nivel de A

phia::testInteractions(modelo.dca,
                       fixed = "A",
                       across = "B",
                       adjustment = "none")
F Test: 
P-value adjustment method: none
               B1      B2 Df Sum of Sq      F    Pr(>F)    
a1        -7.6667 -9.3333  2   148.667 17.265 0.0012520 ** 
a2         3.0000 10.6667  2   181.556 21.084 0.0006466 ***
Residuals                  8    34.444                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Comparación de los niveles de A dentro de cada nivel de B

phia::testInteractions(modelo.dca,
                       fixed = "B",
                       across = "A",
                       adjustment = "none")
F Test: 
P-value adjustment method: none
             Value Df Sum of Sq       F    Pr(>F)    
b1         -0.6667  1     0.667  0.1548 0.7042328    
b2        -10.0000  1   150.000 34.8387 0.0003608 ***
b3         10.0000  1   150.000 34.8387 0.0003608 ***
Residuals           8    34.444                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Plot de interacciones

phia::interactionMeans(model = modelo.dca,
                       factors = c("A","B")) %>%
  plot()

Comparaciones de medias de los niveles de B dentro de cada nivel de A

FA_A1 <- data %>% filter(A=="a1")
FA_A2 <- data %>% filter(A=="a2")

fcomp1 <- function(x){
  comp <- LSD.test(x$rdto, # Cambiar según nombre de variable respuesta
                   x$B, # Cambiar según nombre de variable independiente
                   DFerror = df.residual(modelo.dca), 
                   MSerror = dvmisc::get_mse(modelo.dca),
                   alpha = 0.05,
                   group=TRUE,
                   main = NULL,
                   console=FALSE)
  return(comp[[5]] %>%
           rename("rdto" = "x$rdto") # Cambiar según nombre de variable respuesta
         )
}

Comparaciones de los niveles de B dentro del nivel A1

fcomp1(FA_A1)
        rdto groups
b3 11.333333      a
b1  3.666667      b
b2  2.000000      b

Comparaciones de los niveles de B dentro del nivel A2

fcomp1(FA_A2)
        rdto groups
b2 12.000000      a
b1  4.333333      b
b3  1.333333      b

Comparaciones de medias de los niveles de B dentro de cada nivel de A

FB_B1 <- data %>% filter(B=="b1")
FB_B2 <- data %>% filter(B=="b2")
FB_B3 <- data %>% filter(B=="b3")

fcomp2 <- function(x){
  comp <- LSD.test(x$rdto, # Cambiar según nombre de variable respuesta
                   x$A, # Cambiar según nombre de variable independiente
                   DFerror = df.residual(modelo.dca), 
                   MSerror = dvmisc::get_mse(modelo.dca),
                   alpha = 0.05,
                   group=TRUE,
                   main = NULL,
                   console=FALSE)
  return(comp[[5]] %>%
           rename("rdto" = "x$rdto") # Cambiar según nombre de variable respuesta
         )
}

Comparaciones de los niveles de A dentro del nivel B1

fcomp2(FB_B1)
       rdto groups
a2 4.333333      a
a1 3.666667      a

Comparaciones de los niveles de A dentro del nivel B2

fcomp2(FB_B2)
   rdto groups
a2   12      a
a1    2      b

Comparaciones de los niveles de A dentro del nivel B2

fcomp2(FB_B3)
        rdto groups
a1 11.333333      a
a2  1.333333      b

DCA en arreglo factorial de parcelas divididas con el paquete ExpDes

attach(data)
split2.crd(factor1 = A,
           factor2 =  B,
           repet = rep,
           resp =  rdto,
           quali = c(TRUE,
                     TRUE),
           mcomp = "tukey", 
           fac.names = c("Variedad",
                         "Densidad"),
           sigT = 0.05,
           sigF = 0.05,
           unfold = NULL)
------------------------------------------------------------------------
Legend:
FACTOR 1    (plot):  Variedad 
FACTOR 2 (split-plot):  Densidad 
------------------------------------------------------------------------

------------------------------------------------------------------------
Analysis of Variance Table
------------------------------------------------------------------------
                  DF     SS      MS     Fc   Pr>Fc
Variedad           1   0.22   0.222  0.143 0.72466
Error a            4   6.22   1.556               
Densidad           2  29.78  14.889  3.458 0.08274
Variedad*Densidad  2 300.44 150.222 34.890 0.00011
Error b            8  34.44   4.306               
Total             17 371.11                       
------------------------------------------------------------------------
CV 1 = 21.58649 %
CV 2 = 35.91317 %

------------------------------------------------------------------------
Shapiro-Wilk normality test (Error b)
p-value:  0.8685814 
According to Shapiro-Wilk normality test at 5% of significance, residuals can be considered normal.
------------------------------------------------------------------------



Significant interaction: analyzing the interaction
------------------------------------------------------------------------

Analyzing  Variedad  inside of each level of  Densidad 
------------------------------------------------------------------------
                              DF         SS         MS        Fc  p.value
Variedad : Densidad b1   1.00000   0.666667   0.666667  0.196721 0.666407
Variedad : Densidad b2   1.00000 150.000000 150.000000 44.262289 0.000046
Variedad : Densidad b3   1.00000 150.000000 150.000000 44.262289 0.000046
Pooled Error            10.46818  35.475483   3.388889        NA       NA
------------------------------------------------------------------------


 Variedad inside of Densidad b1
------------------------------------------------------------------------
According to F test, the means of this factor are not distinct.
------------------------------------------------------------------------
  Levels    Means
1     a1 3.666667
2     a2 4.333333
------------------------------------------------------------------------

 Variedad inside of Densidad b2
------------------------------------------------------------------------
Tukey's test
------------------------------------------------------------------------
Groups Treatments Means
a    a2      12 
 b   a1      2 
------------------------------------------------------------------------

 Variedad inside of Densidad b3
------------------------------------------------------------------------
Tukey's test
------------------------------------------------------------------------
Groups Treatments Means
a    a1      11.33333 
 b   a2      1.333333 
------------------------------------------------------------------------


Analyzing  Densidad  inside of each level of  Variedad 
------------------------------------------------------------------------
                        DF        SS        MS       Fc  p.value
Densidad : Variedad a1   2 148.66667 74.333333 17.26451 0.001252
Densidad : Variedad a2   2 181.55556 90.777778 21.08387 0.000647
Error b                  8  34.44444  4.305555       NA       NA
------------------------------------------------------------------------


 Densidad inside of Variedad a1
------------------------------------------------------------------------
Tukey's test
------------------------------------------------------------------------
Groups Treatments Means
a    b3      11.33333 
 b   b1      3.666667 
 b   b2      2 
------------------------------------------------------------------------
------------------------------------------------------------------------


 Densidad inside of Variedad a2
------------------------------------------------------------------------
Tukey's test
------------------------------------------------------------------------
Groups Treatments Means
a    b2      12 
 b   b1      4.333333 
 b   b3      1.333333 
------------------------------------------------------------------------
------------------------------------------------------------------------

Importante

El paquete ExpDes usa la expresión “rep:A”, es decir, considera la interacción como efecto aleatorio.

Diseño de bloques completos al azar en arreglo de parcelas divididas

Planeamiento


Crear un libro de campo con el paquete agricolae


trt1 <- c("Ventura","Biloxi","Emerald")
trt2 <- c("50 kg.ha N","100 kg.ha N", "150 kg.ha N")

r <- 5

salida <- agricolae::design.split(trt1 = trt1,
                                  trt2 = trt2,
                                  r = r,
                                  design = "rcbd",
                                  serie = 3,
                                  seed = 123,
                                  kinds = "Super-Duper",
                                  randomization = TRUE)
salida$book %>% 
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)

Guardar el libro generado

write.table(salida$book,
            "books/rcbdspplot.txt",
            row.names = FALSE,
            sep = "\t")

write.xlsx(salida$book,
           "books/rcbdspplot.xlsx",
           sheetName = "book",
           append = FALSE,
           row.names = FALSE)

Guardar el libro de campo generado

write.table(salida %>% zigzag(),
            "books/rcbdspplot.txt",
            row.names = FALSE,
            sep = "\t")

write.xlsx(salida %>% zigzag(),
           "books/rcbdspplot.xlsx",
           sheetName = "book",
           append = FALSE,
           row.names = FALSE)
agricolaeplotr::plot_split_rcbd(
  design = salida,
  factor_name_1 = "trt1",
  factor_name_2 = "trt2",
  y = "block",
  subplots = FALSE,
  reverse_y = TRUE) +
  labs(fill = "Variedades",
       x = "Columnas",
       y = "Bloques")
agricolaeplotr::plot_split_rcbd(
  design = salida,
  factor_name_1 = "trt1",
  factor_name_2 = "trt2",
  y = "block",
  subplots = TRUE,
  reverse_y = TRUE) +
  labs(fill = "Dosis de Nitrógeno",
       x = "Columnas",
       y = "Bloques")

Crear un libro de campo con el paquete edibble


menu_split()
design("Split-Plot Design | Split-Unit Design") %>%
  set_units(mainplot = 9,
             subplot = nested_in(mainplot, 6)) %>%
  set_trts(trt1 = 3,
           trt2 = 6) %>%
  allot_trts(trt1 ~ mainplot,
             trt2 ~ subplot) %>%
  assign_trts("random", seed = 332) %>%
  serve_table()
rcbd <- takeout(menu_split(t1 = 3,
                           t2 = 3,
                           r = 5,
                           seed = 123))
rcbd %>% 
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)
rcbd2 <- design("Split-Plot Design | Split-Unit Design") %>%
  set_units(block = 5,
            mainplot = nested_in(block, 3),
            subplot = nested_in(mainplot, 3)) %>%
  set_trts(trt1 = trt1,
           trt2 = trt2) %>%
  allot_trts(trt1 ~ mainplot,
             trt2 ~ subplot) %>%
  assign_trts("random", seed = 123) %>%
  serve_table()
rcbd2 %>% 
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)
write.table(rcbd2 %>% as.data.frame(),
            "books/rcbdspplot.txt",
            row.names = FALSE,
            sep = "\t")

write.xlsx(rcbd2 %>% as.data.frame(),
           "books/rcbdspplot.xlsx",
           sheetName = "book",
           append = FALSE,
           row.names = FALSE)
deggust::autoplot(rcbd2)
plot(rcbd2)

Análisis de DBCA en arreglo factorial de parcelas divididas


Importación de datos


archivos <- list.files(pattern = "datos split plot.xlsx", 
                       full.names = TRUE,
                       recursive = TRUE)

# Importación
data <- readxl::read_xlsx(archivos,
                           sheet = "dbca")

# Preprocesamiento

data <- data %>%
  mutate_if(is.character, factor) %>%
  mutate(bloque = factor(bloque))

Creación del modelo lineal


modelo.dbca1 <- lm(rdto ~ A * B + bloque/A + bloque, data = data)
modelo.dbca2 <- lm(rdto ~ A * B + bloque:A + bloque, data = data)
modelo.dbca3 <- lm(rdto ~ A + B + bloque/A + bloque, data = data)
modelo.dbca4 <- lm(rdto ~ A + B + bloque:A + bloque, data = data)
broom::glance(modelo.dbca1) %>%
  bind_rows(broom::glance(modelo.dbca2),
            broom::glance(modelo.dbca3),
            broom::glance(modelo.dbca4)) %>%
  dplyr::mutate(Modelo = c("A * B + bloque + rep/A",
                           "A * B + bloque + rep:A",
                           "A + B + bloque + rep/A",
                           "A + B + bloque + rep:A")) %>%
  dplyr::select(Modelo, AIC, BIC) %>%
  dplyr::arrange(BIC) %>%
  dplyr::mutate(Mérito = 1:n()) %>%
  dplyr::relocate(Mérito, Modelo) %>%
  gt()
Mérito Modelo AIC BIC
1 A * B + bloque + rep/A 84.76335 94.55744
2 A * B + bloque + rep:A 84.76335 94.55744
3 A + B + bloque + rep/A 121.70347 129.71682
4 A + B + bloque + rep:A 121.70347 129.71682

Definición del modelo


modelo.dbca <- lm(rdto ~ A * B + bloque/A + bloque, data = data)

\[Y_i = \beta_0 + \beta_1*Bloq_{II} + \beta_2*Bloq_{III} + \beta_3*A_2 + \beta_4*B_2 + \beta_5*B_3 + \beta_6*A_2*B_2 + \beta_7*A_2*B_3 + \beta_8*A_2*Bloq_{II} + \beta_9*A_2*Bloq_{III} + \epsilon_i\]

\[\hat{Y}_i = \beta_0 + \beta_1*Bloq_{II} + \beta_2*Bloq_{III} + \beta_3*A_2 + \beta_4*B_2 + \beta_5*B_3 + \beta_6*A_2*B_2 + \beta_7*A_2*B_3 + \beta_8*A_2*Bloq_{II} + \beta_9*A_2*Bloq_{III}\]

summary(modelo.dbca)

Call:
lm(formula = rdto ~ A * B + bloque/A + bloque, data = data)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.3333 -0.7778  0.1111  0.9167  3.0000 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept)    2.667      1.547   1.724  0.12296   
Aa2            1.778      2.187   0.813  0.43985   
Bb2           -1.667      1.694  -0.984  0.35406   
Bb3            7.667      1.694   4.525  0.00194 **
bloque2        1.333      1.694   0.787  0.45397   
bloque3        1.667      1.694   0.984  0.35406   
Aa2:Bb2        9.333      2.396   3.895  0.00457 **
Aa2:Bb3      -10.667      2.396  -4.452  0.00213 **
Aa2:bloque2   -1.000      2.396  -0.417  0.68739   
Aa2:bloque3   -2.333      2.396  -0.974  0.35865   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.075 on 8 degrees of freedom
Multiple R-squared:  0.9072,    Adjusted R-squared:  0.8028 
F-statistic: 8.688 on 9 and 8 DF,  p-value: 0.002851

Verificación visual de los supuestos del modelo


performance::check_model(modelo.dbca)
ggResidpanel::resid_panel(modelo.dbca)
influence.measures(modelo.dbca)
Influence measures of
     lm(formula = rdto ~ A * B + bloque/A + bloque, data = data) :

      dfb.1_ dfb.Aa2   dfb.Bb2   dfb.Bb3  dfb.blq2  dfb.blq3 dfb.A2.B2
1   1.07e+00 -0.7582 -5.87e-01 -5.87e-01 -5.87e-01 -5.87e-01  4.15e-01
2   0.00e+00  0.0000  0.00e+00  0.00e+00  0.00e+00  0.00e+00  0.00e+00
3  -4.29e-01  0.3033 -9.78e-17 -5.87e-01  5.87e-01  5.87e-01  3.46e-17
4  -2.41e-16  0.9063 -4.59e-16  1.35e-16  2.50e-16  2.47e-16 -4.96e-01
5  -8.93e-17 -0.5362  3.32e-16  1.46e-16  2.81e-16 -9.98e-17 -7.34e-01
6  -7.00e-17  0.1200 -5.81e-17  7.38e-33  1.11e-16  1.19e-16  2.74e-17
7   3.13e-01 -0.2212 -4.28e-01 -4.28e-01  4.28e-01 -2.01e-16  3.03e-01
8  -1.02e-01  0.0723  2.80e-01 -1.91e-17  2.80e-01  7.52e-17 -1.98e-01
9   2.79e-01 -0.1970  3.18e-16 -7.63e-01 -7.63e-01 -3.64e-16 -2.25e-16
10  1.41e-17 -0.1697  1.68e-16  6.32e-17 -9.09e-17 -6.32e-17  2.32e-01
11 -1.51e-17 -0.1813  1.94e-16  3.66e-17  9.15e-17 -7.03e-17  4.96e-01
12  1.41e-17  0.0849 -1.12e-16 -3.16e-17  3.58e-17 -1.32e-18  1.35e-16
13 -8.79e-01  0.6216  1.20e+00  1.20e+00  5.01e-16 -1.20e+00 -8.51e-01
14  1.02e-01 -0.0723 -2.80e-01  8.64e-17 -1.17e-16 -2.80e-01  1.98e-01
15 -7.07e-01  0.4997 -8.06e-16  1.94e+00  3.22e-16  1.94e+00  6.84e-16
16  0.00e+00 -0.1697  1.96e-16  6.32e-17 -2.77e-17 -7.37e-17  2.32e-01
17  5.00e-18 -0.0600  9.46e-17  3.44e-17 -6.30e-17 -7.45e-17  1.64e-01
18  1.78e-17 -0.0238  1.15e-17 -1.48e-33 -1.97e-17 -2.66e-17 -1.63e-17
   dfb.A2.B3  dfb.A2.2  dfb.A2.3     dffit   cov.r   cook.d   hat inf
1   4.15e-01  4.15e-01  4.15e-01  1.07e+00 2.48880 1.16e-01 0.556   *
2   0.00e+00  0.00e+00  0.00e+00 -7.55e-16 8.55268 6.52e-32 0.556   *
3   4.15e-01 -4.15e-01 -4.15e-01 -1.07e+00 2.48880 1.16e-01 0.556    
4  -4.96e-01 -4.96e-01 -4.96e-01  1.28e+00 1.53070 1.58e-01 0.556    
5  -2.71e-16  7.34e-01  7.34e-01 -1.90e+00 0.27401 2.91e-01 0.556    
6   1.64e-01 -1.64e-01 -1.64e-01  4.24e-01 6.97667 2.02e-02 0.556   *
7   3.03e-01 -3.03e-01  1.46e-17  7.82e-01 4.35231 6.53e-02 0.556    
8   5.24e-17 -1.98e-01 -9.52e-18  5.11e-01 6.37016 2.90e-02 0.556   *
9   5.39e-01  5.39e-01  3.89e-16 -1.39e+00 1.15490 1.81e-01 0.556    
10  2.32e-01 -2.32e-01  1.68e-17 -6.00e-01 5.71482 3.95e-02 0.556   *
11 -7.16e-17  4.96e-01 -7.16e-17  1.28e+00 1.53070 1.58e-01 0.556    
12 -2.32e-01 -2.32e-01 -1.68e-17 -6.00e-01 5.71482 3.95e-02 0.556   *
13 -8.51e-01 -2.13e-16  8.51e-01 -2.20e+00 0.10552 3.56e-01 0.556   *
14 -1.35e-16  3.30e-17  1.98e-01 -5.11e-01 6.37016 2.90e-02 0.556   *
15 -1.37e+00  0.00e+00 -1.37e+00  3.53e+00 0.00121 5.88e-01 0.556   *
16  2.32e-01  1.93e-17 -2.32e-01 -6.00e-01 5.71482 3.95e-02 0.556   *
17 -4.48e-17 -1.37e-17  1.64e-01  4.24e-01 6.97667 2.02e-02 0.556   *
18  6.52e-02  1.09e-17  6.52e-02  1.68e-01 8.28075 3.23e-03 0.556   *
influenceIndexPlot(modelo.dbca)

Cumplimiento de supuestos del modelo lineal general


Independencia de residuos

\(H_0: \text{Los residuos del rendimiento son completamente aleatorios e independientes}\)

\(H_1: \text{Los residuos del rendimiento no son completamente aleatorios e independientes}\)

durbinWatsonTest(modelo.dbca,
                 reps = 5000,
                 max.lag = 5)
 lag Autocorrelation D-W Statistic p-value
   1     -0.25591398      2.458781  0.8496
   2     -0.35161290      2.641219  0.3892
   3      0.07741935      1.713978  0.9088
   4      0.26845878      1.000358  0.4160
   5     -0.17275986      1.740502  0.2492
 Alternative hypothesis: rho[lag] != 0
dwtest(modelo.dbca, alternative = "two.sided")

    Durbin-Watson test

data:  modelo.dbca
DW = 2.4588, p-value = 0.8145
alternative hypothesis: true autocorrelation is not 0

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los residuos del rendimiento son completamente aleatorios e independientes.

Normalidad de residuos

\(H_0: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

\(H_1: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

shapiro.test(rstudent(modelo.dbca))

    Shapiro-Wilk normality test

data:  rstudent(modelo.dbca)
W = 0.95347, p-value = 0.482
ad.test(rstudent(modelo.dbca))

    Anderson-Darling normality test

data:  rstudent(modelo.dbca)
A = 0.28753, p-value = 0.5783
lillie.test(rstudent(modelo.dbca))

    Lilliefors (Kolmogorov-Smirnov) normality test

data:  rstudent(modelo.dbca)
D = 0.12222, p-value = 0.6786
ks.test(rstudent(modelo.dbca), "pnorm",
        alternative = "two.sided")

    Exact one-sample Kolmogorov-Smirnov test

data:  rstudent(modelo.dbca)
D = 0.12079, p-value = 0.9274
alternative hypothesis: two-sided
cvm.test(rstudent(modelo.dbca))

    Cramer-von Mises normality test

data:  rstudent(modelo.dbca)
W = 0.035902, p-value = 0.7384
pearson.test(rstudent(modelo.dbca))

    Pearson chi-square normality test

data:  rstudent(modelo.dbca)
P = 3, p-value = 0.5578
sf.test(rstudent(modelo.dbca))

    Shapiro-Francia normality test

data:  rstudent(modelo.dbca)
W = 0.94303, p-value = 0.2775

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la distribución de los residuos del rendimiento es similar a la función normal o gaussiana.

Homocedasticidad

\(H_0\): La varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento

\(H_1\): La varianza del rendimiento no es constante con respecto a los valores ajustados del rendimiento

ncvTest(modelo.dbca)
Non-constant Variance Score Test 
Variance formula: ~ fitted.values 
Chisquare = 4.009865, Df = 1, p = 0.045235
bptest(modelo.dbca)

    studentized Breusch-Pagan test

data:  modelo.dbca
BP = 14.223, df = 9, p-value = 0.1146
bptest(modelo.dbca, studentize = F)

    Breusch-Pagan test

data:  modelo.dbca
BP = 10.037, df = 9, p-value = 0.3475
olsrr::ols_test_breusch_pagan(modelo.dbca)

 Breusch Pagan Test for Heteroskedasticity
 -----------------------------------------
 Ho: the variance is constant            
 Ha: the variance is not constant        

              Data               
 --------------------------------
 Response : rdto 
 Variables: fitted values of rdto 

        Test Summary          
 -----------------------------
 DF            =    1 
 Chi2          =    4.009865 
 Prob > Chi2   =    0.04523478 

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento.

Recomendación. Debido a que se cumple con el supuesto de homocedasticidad, para evaluar los efectos de los tratamientos con respecto al rendimiento, se debe proceder a realizar el análisis de varianza.

Estadísticas globales

modelo.dbca %>% gvlma()

Call:
lm(formula = rdto ~ A * B + bloque/A + bloque, data = data)

Coefficients:
(Intercept)          Aa2          Bb2          Bb3      bloque2      bloque3  
      2.667        1.778       -1.667        7.667        1.333        1.667  
    Aa2:Bb2      Aa2:Bb3  Aa2:bloque2  Aa2:bloque3  
      9.333      -10.667       -1.000       -2.333  


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = .) 

                     Value p-value                Decision
Global Stat        3.20107  0.5248 Assumptions acceptable.
Skewness           0.07893  0.7788 Assumptions acceptable.
Kurtosis           0.25987  0.6102 Assumptions acceptable.
Link Function      2.78083  0.0954 Assumptions acceptable.
Heteroscedasticity 0.08145  0.7753 Assumptions acceptable.

Análisis de varianza

\[Y_{ijk} = \mu + \tau_{i} + \gamma_{k} + \text{Error}(\tau\gamma)_{ik} + \beta_{j} + (\tau\beta)_{ij} + \epsilon_{ijk}\]

\[\hat{Y}_{ijk} = \mu + \tau_{i} + \gamma_{k} + \text{Error}(\tau\gamma)_{ik} + \beta_{j} + (\tau\beta)_{ij} \]

Dónde:

\(Y_{ijk}\) = Valor observado de la variable respuesta.

\(\hat{Y}_{ijk}\) = Valor ajustado de la variable respuesta.

\(\mu\) = Promedio observado de la variable respuesta.

\(\tau_{i}\) = Efecto del i-ésimo nivel del factor A.

\(\gamma_{k}\) = Efecto del k-ésimo nivel del factor Bloque.

\(\text{Error}(\tau\text{rep})_{ik}\) = Residuo observado del modelo a nivel de parcelas principales.

\(\beta_{j}\) = Efecto del j-ésimo nivel del factor B.

\((\tau\beta)_{ij}\) = Efecto de interacción del factor A x factor B dentro de los niveles ij.

\(\epsilon_{ijk}\) = Residuo observado del modelo a nivel de subparcelas.

Pruebas de hipótesis

Para el factor A (Variedad):

\(H_0: \tau_{A1} = \tau_{A2} = 0\)

\(H_1: \text{En al menos un nivel del factor A el } \tau \text{ es diferente a los demás.}\)

\(H_1: \tau_i \neq 0\text{; en al menos un nivel del factor A.}\)

Para el factor B (Densidad):

\(H_0: \beta_{B1} = \beta_{B2} = \beta_{B3} = 0\)

\(H_1: \text{En al menos un nivel del factor B el } \beta \text{ es diferente a los demás.}\)

\(H_1: \beta_j \neq 0\text{; en al menos un nivel del factor B.}\)

Para la interacción entre factor A y factor B:

\(H_0: (\tau\beta)_{A1B1} = (\tau\beta)_{A1B2} = (\tau\beta)_{A1B3} = (\tau\beta)_{A2B1} = (\tau\beta)_{A2B2} = (\tau\beta)_{A2B3} = 0\)

\(H_1: \text{En al menos una interacción entre el factor A y el factor B el } (\tau\beta) \text{ es diferente a los demás.}\)

\(H_1: (\tau\beta)_{ij} \neq 0\text{; en al menos una interacción entre el factor A y el factor B.}\)

Precaución

  • Si se ignora el diseño experimental, se obtienen los siguientes resultados, incorrectos. Observe que los grados de libertad del error es mayor, lo que facilita la detección de diferencias que en realidad no existen.
anova(modelo.dbca, test = "F")
Analysis of Variance Table

Response: rdto
          Df  Sum Sq Mean Sq F value    Pr(>F)    
A          1   0.222   0.222  0.0516 0.8259782    
B          2  29.778  14.889  3.4581 0.0827438 .  
bloque     2   2.111   1.056  0.2452 0.7882486    
A:B        2 300.444 150.222 34.8903 0.0001119 ***
A:bloque   2   4.111   2.056  0.4774 0.6369845    
Residuals  8  34.444   4.306                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Importante

Necesitamos especificar correctamente el término de error para el factor A. Debe tenerse en cuenta que la forma del Error es “Error(A:parcelagrande)” en el caso de efectos aleatorios o “Error(A:bloque)” para el caso de efectos fijos y puede cambiar dependiendo de la disposición de los datos. La clave es conocer los grados de libertad correcto para saber que se obtienen los resultados correctos.

aov(rdto ~ A * B + bloque + Error(bloque/A), data = data) -> aov.dbca
summary(aov.dbca)

Error: bloque
       Df Sum Sq Mean Sq
bloque  2  2.111   1.056

Error: bloque:A
          Df Sum Sq Mean Sq F value Pr(>F)
A          1  0.222  0.2222   0.108  0.774
Residuals  2  4.111  2.0556               

Error: Within
          Df Sum Sq Mean Sq F value   Pr(>F)    
B          2  29.78   14.89   3.458 0.082744 .  
A:B        2 300.44  150.22  34.890 0.000112 ***
Residuals  8  34.44    4.31                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
data %>% with(agricolae::sp.plot(block = bloque,
                                 pplot = A,
                                 splot = B,
                                 Y = rdto))

ANALYSIS SPLIT PLOT:  rdto 
Class level information

A   :  a1 a2 
B   :  b1 b2 b3 
bloque  :  1 2 3 

Number of observations:  18 

Analysis of Variance Table

Response: rdto
       Df  Sum Sq Mean Sq F value    Pr(>F)    
bloque  2   2.111   1.056     NaN       NaN    
A       1   0.222   0.222  0.1081 0.7735446    
Ea      2   4.111   2.056     NaN       NaN    
B       2  29.778  14.889  3.4581 0.0827438 .  
A:B     2 300.444 150.222 34.8903 0.0001119 ***
Eb      8  34.444   4.306     NaN       NaN    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

cv(a) = 24.8 %, cv(b) = 35.9 %, Mean = 5.777778 
broom::tidy(aov.dbca)
# A tibble: 6 × 7
  stratum  term         df   sumsq  meansq statistic   p.value
  <chr>    <chr>     <dbl>   <dbl>   <dbl>     <dbl>     <dbl>
1 bloque   bloque        2   2.11    1.06     NA     NA       
2 bloque:A A             1   0.222   0.222     0.108  0.774   
3 bloque:A Residuals     2   4.11    2.06     NA     NA       
4 Within   B             2  29.8    14.9       3.46   0.0827  
5 Within   A:B           2 300.    150.       34.9    0.000112
6 Within   Residuals     8  34.4     4.31     NA     NA       

Valor de la tabla de F para el factor A con una significancia de 0.05.

qf(0.95, 1, 2)
[1] 18.51282

Valor de la tabla de F para el factor B con una significancia de 0.05.

qf(0.95, 2, 8)
[1] 4.45897

Valor de la tabla de F para la interacción A:B con una significancia de 0.05.

qf(0.95, 2, 8)
[1] 4.45897
shadeDist(qf(0.95, 2, 8), "df",2, 8, lower.tail = F)

Conclusión.

Con respecto al Factor A: A un nivel de significancia de 0.05, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los niveles del factor A tienen un efecto sobre el rendimiento estadísticamente similar a 0.

Con respecto al Factor B: A un nivel de significancia de 0.05, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los niveles del factor B tienen un efecto sobre el rendimiento estadísticamente similar a 0.

Con respecto a la interacción entre el Factor A y Factor B: A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos una interacción entre un nivel del factor A y un nivel del factor B existe un efecto de antagonismo o sinergismo sobre el rendimiento.

agricolae::cv.model(modelo.dbca)
[1] 35.91317

Comparaciones de medias para los efectos principales del Factor A

data %>% with(LSD.test(
  rdto, # Cambiar según nombre de variable respuesta
  A, # Cambiar según nombre de variable independiente
  DFerror = get_df_ea_spplot(aov.dbca), 
  MSerror = get_mse_ea_spplot(aov.dbca),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: rdto ~ A

LSD t Test for rdto 

Mean Square Error:  2.055556 

A,  means and individual ( 95 %) CI

       rdto      std r      LCL      UCL Min Max
a1 5.666667 4.690416 9 3.610399 7.722934   1  15
a2 5.888889 4.935698 9 3.832621 7.945157   1  14

Alpha: 0.05 ; DF Error: 2
Critical Value of t: 4.302653 

least Significant Difference: 2.908002 

Treatments with the same letter are not significantly different.

       rdto groups
a2 5.888889      a
a1 5.666667      a

Comparaciones de medias para los efectos principales del Factor B

data %>% with(LSD.test(
  rdto, # Cambiar según nombre de variable respuesta
  B, # Cambiar según nombre de variable independiente
  DFerror = df.residual(modelo.dbca), 
  MSerror = dvmisc::get_mse(modelo.dbca),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: rdto ~ B

LSD t Test for rdto 

Mean Square Error:  4.305556 

B,  means and individual ( 95 %) CI

       rdto      std r      LCL      UCL Min Max
b1 4.000000 1.414214 6 2.046565 5.953435   2   6
b2 7.000000 5.656854 6 5.046565 8.953435   1  14
b3 6.333333 5.853774 6 4.379898 8.286769   1  15

Alpha: 0.05 ; DF Error: 8
Critical Value of t: 2.306004 

least Significant Difference: 2.762575 

Treatments with the same letter are not significantly different.

       rdto groups
b2 7.000000      a
b3 6.333333     ab
b1 4.000000      b

Precaución

Si el análisis de varianza arroja que los niveles de un factor son estadísticamente similares entre sí, entonces no es necesario realizar una prueba de comparación de medias y por ende todos estos niveles pertenecen a un mismo grupo de significancia “a”.

Comparaciones de medias para las interacciones

Para los niveles del factor A dentro del nivel B1:

  • A1 vs A2:

\(H_0: \mu_{A1} - \mu_{A2} = 0\)

\(H_1: \mu_{A1} - \mu_{A2} \neq 0\)

Para los niveles del factor B dentro del nivel A1:

  • B1 vs B2:

\(H_0: \mu_{B1} - \mu_{B2} = 0\)

\(H_1: \mu_{B1} - \mu_{B2} \neq 0\)

  • B1 vs B3:

\(H_0: \mu_{B1} - \mu_{B3} = 0\)

\(H_1: \mu_{B1} - \mu_{B3} \neq 0\)

  • B2 vs B3:

\(H_0: \mu_{B2} - \mu_{B3} = 0\)

\(H_1: \mu_{B2} - \mu_{B3} \neq 0\)

NOTA: Repetir este proceso para cada nivel de A y cada nivel de B.

Análisis de varianza para interacción de dos factores con el paquete phia

Comparación de los niveles de B dentro de cada nivel de A

phia::testInteractions(modelo.dbca,
                       fixed = "A",
                       across = "B",
                       adjustment = "none")
F Test: 
P-value adjustment method: none
               B1      B2 Df Sum of Sq      F    Pr(>F)    
a1        -7.6667 -9.3333  2   148.667 17.265 0.0012520 ** 
a2         3.0000 10.6667  2   181.556 21.084 0.0006466 ***
Residuals                  8    34.444                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Comparación de los niveles de A dentro de cada nivel de B

phia::testInteractions(modelo.dbca,
                       fixed = "B",
                       across = "A",
                       adjustment = "none")
F Test: 
P-value adjustment method: none
             Value Df Sum of Sq       F    Pr(>F)    
b1         -0.6667  1     0.667  0.1548 0.7042328    
b2        -10.0000  1   150.000 34.8387 0.0003608 ***
b3         10.0000  1   150.000 34.8387 0.0003608 ***
Residuals           8    34.444                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Plot de interacciones

phia::interactionMeans(model = modelo.dbca,
                       factors = c("A","B")) %>%
  plot()

Comparaciones de medias de los niveles de B dentro de cada nivel de A

FA_A1 <- data %>% filter(A=="a1")
FA_A2 <- data %>% filter(A=="a2")

fcomp1 <- function(x){
  comp <- LSD.test(x$rdto, # Cambiar según nombre de variable respuesta
                   x$B, # Cambiar según nombre de variable independiente
                   DFerror = df.residual(modelo.dbca), 
                   MSerror = dvmisc::get_mse(modelo.dbca),
                   alpha = 0.05,
                   group=TRUE,
                   main = NULL,
                   console=FALSE)
  return(comp[[5]] %>%
           rename("rdto" = "x$rdto") # Cambiar según nombre de variable respuesta
         )
}

Comparaciones de los niveles de B dentro del nivel A1

fcomp1(FA_A1)
        rdto groups
b3 11.333333      a
b1  3.666667      b
b2  2.000000      b

Comparaciones de los niveles de B dentro del nivel A2

fcomp1(FA_A2)
        rdto groups
b2 12.000000      a
b1  4.333333      b
b3  1.333333      b

Comparaciones de medias de los niveles de B dentro de cada nivel de A

FB_B1 <- data %>% filter(B=="b1")
FB_B2 <- data %>% filter(B=="b2")
FB_B3 <- data %>% filter(B=="b3")

fcomp2 <- function(x){
  comp <- LSD.test(x$rdto, # Cambiar según nombre de variable respuesta
                   x$A, # Cambiar según nombre de variable independiente
                   DFerror = df.residual(modelo.dbca), 
                   MSerror = dvmisc::get_mse(modelo.dbca),
                   alpha = 0.05,
                   group=TRUE,
                   main = NULL,
                   console=FALSE)
  return(comp[[5]] %>%
           rename("rdto" = "x$rdto") # Cambiar según nombre de variable respuesta
         )
}

Comparaciones de los niveles de A dentro del nivel B1

fcomp2(FB_B1)
       rdto groups
a2 4.333333      a
a1 3.666667      a

Comparaciones de los niveles de A dentro del nivel B2

fcomp2(FB_B2)
   rdto groups
a2   12      a
a1    2      b

Comparaciones de los niveles de A dentro del nivel B3

fcomp2(FB_B3)
        rdto groups
a1 11.333333      a
a2  1.333333      b

DBCA en arreglo factorial de parcelas divididas con el paquete ExpDes

attach(data)
split2.rbd(factor1 = A,
           factor2 = B,
           block = bloque,
           resp =  rdto,
           quali = c(TRUE,
                     TRUE),
           mcomp = "tukey", 
           fac.names = c("Variedad",
                         "Densidad"),
           sigT = 0.05,
           sigF = 0.05,
           unfold = 1)
------------------------------------------------------------------------
Legend:
FACTOR 1 (plot):  Variedad 
FACTOR 2 (split-plot):  Densidad 
------------------------------------------------------------------------

------------------------------------------------------------------------
Analysis of Variance Table
------------------------------------------------------------------------
                  DF     SS      MS     Fc  Pr(>Fc)    
Variedad           1   0.22   0.222  0.108 0.773545    
Block              2   2.11   1.056  0.514 0.660714    
Error a            2   4.11   2.056                    
Densidad           2  29.78  14.889  3.458 0.082744 .  
Variedad*Densidad  2 300.44 150.222 34.890 0.000112 ***
Error b            8  34.44   4.306                    
Total             17 371.11                            
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------------------------------------
CV 1 = 24.8144 %
CV 2 = 35.91317 %

No significant interaction: analyzing the simple effects
------------------------------------------------------------------------
Variedad
According to F test, the means of this factor are not different.
------------------------------------------------------------------------
  Levels    Means
1     a1 5.666667
2     a2 5.888889
------------------------------------------------------------------------
Densidad
According to F test, the means of this factor are not different.
------------------------------------------------------------------------
  Levels    Means
1     b1 4.000000
2     b2 7.000000
3     b3 6.333333
------------------------------------------------------------------------



Significant interaction: analyzing the interaction
------------------------------------------------------------------------

Analyzing  Variedad  inside of each level of  Densidad 
------------------------------------------------------------------------
                              DF         SS         MS       Fc  p.value
Variedad : Densidad b1  1.000000   0.666667   0.666667  0.18750 0.674199
Variedad : Densidad b2  1.000000 150.000000 150.000000 42.18749 0.000069
Variedad : Densidad b3  1.000000 150.000000 150.000000 42.18749 0.000069
Pooled Error            9.996678  35.543748   3.555556       NA       NA
------------------------------------------------------------------------


 Variedad inside of Densidad b1
------------------------------------------------------------------------
According to F test, the means of this factor are not different.
------------------------------------------------------------------------
  Levels    Means
1     a1 3.666667
2     a2 4.333333
------------------------------------------------------------------------

 Variedad inside of Densidad b2
------------------------------------------------------------------------
Tukey's test
------------------------------------------------------------------------
Groups Treatments Means
a    a2      12 
 b   a1      2 
------------------------------------------------------------------------

 Variedad inside of Densidad b3
------------------------------------------------------------------------
Tukey's test
------------------------------------------------------------------------
Groups Treatments Means
a    a1      11.33333 
 b   a2      1.333333 
------------------------------------------------------------------------


Analyzing  Densidad  inside of each level of  Variedad 
------------------------------------------------------------------------
                        DF        SS        MS       Fc  p.value
Densidad : Variedad a1   2 148.66667 74.333333 17.26451 0.001252
Densidad : Variedad a2   2 181.55556 90.777778 21.08387 0.000647
Error b                  8  34.44444  4.305555       NA       NA
------------------------------------------------------------------------


 Densidad inside of Variedad a1
------------------------------------------------------------------------
Tukey's test
------------------------------------------------------------------------
Groups Treatments Means
a    b3      11.33333 
 b   b1      3.666667 
 b   b2      2 
------------------------------------------------------------------------
------------------------------------------------------------------------


 Densidad inside of Variedad a2
------------------------------------------------------------------------
Tukey's test
------------------------------------------------------------------------
Groups Treatments Means
a    b2      12 
 b   b1      4.333333 
 b   b3      1.333333 
------------------------------------------------------------------------
------------------------------------------------------------------------

Importante

El paquete ExpDes usa la expresión “bloque:A”, es decir, considera la interacción como efecto aleatorio.

Diseño cuadrado latino en arreglo de parcelas divididas

Planeamiento


Crear un libro de campo con el paquete agricolae


trt1 <- c("Ventura","Biloxi","Emerald")
trt2 <- c("50 kg.ha N","100 kg.ha N")

salida <- agricolae::design.split(trt1 = trt1,
                                  trt2 = trt2,
                                  design = "lsd",
                                  serie = 3,
                                  seed = 123,
                                  kinds = "Super-Duper",
                                  randomization = TRUE)
salida$book %>% 
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)

Guardar el libro generado

write.table(salida$book,
            "books/lsdspplot.txt",
            row.names = FALSE,
            sep = "\t")

write.xlsx(salida$book,
           "books/lsdspplot.xlsx",
           sheetName = "book",
           append = FALSE,
           row.names = FALSE)

Guardar el libro de campo generado

write.table(salida %>% zigzag(),
            "books/lsdspplot.txt",
            row.names = FALSE,
            sep = "\t")

write.xlsx(salida %>% zigzag(),
           "books/lsdspplot.xlsx",
           sheetName = "book",
           append = FALSE,
           row.names = FALSE)
agricolaeplotr::plot_split_lsd(
  design = salida,
  factor_name_1 = "trt1",
  factor_name_2 = "trt2",
  subplots = FALSE,
  reverse_y = TRUE) +
  labs(fill = "Variedades",
       x = "Columnas",
       y = "Filas")
agricolaeplotr::plot_split_lsd(
  design = salida,
  factor_name_1 = "trt1",
  factor_name_2 = "trt2",
  subplots = TRUE,
  reverse_y = TRUE) +
  labs(fill = "Dosis de Nitrógeno",
       x = "Columnas",
       y = "Bloques")

Análisis de DCL en arreglo factorial de parcelas divididas


Importación de datos


archivos <- list.files(pattern = "datos split plot.xlsx", 
                       full.names = TRUE,
                       recursive = TRUE)

# Importación
data <- readxl::read_xlsx(archivos,
                           sheet = "dcl")

# Preprocesamiento

data <- data %>%
  mutate_if(is.character, factor) %>%
  mutate(row = factor(row),
         col = factor(col))
attach(data)

Creación del modelo lineal


modelo.dcl1 <- lm(PESO ~ row + col + FA * FB + row/FA, data = data)
modelo.dcl2 <- lm(PESO ~ row + col + FA + FB + row/FA, data = data)
modelo.dcl3 <- lm(PESO ~ row + FA * FB + row/FA, data = data)
modelo.dcl4 <- lm(PESO ~ row + FA + FB + row/FA, data = data)
modelo.dcl5 <- lm(PESO ~ col + FA * FB + row/FA, data = data)
modelo.dcl6 <- lm(PESO ~ col + FA + FB + row/FA, data = data)
broom::glance(modelo.dcl1) %>%
  bind_rows(broom::glance(modelo.dcl2),
            broom::glance(modelo.dcl3),
            broom::glance(modelo.dcl4),
            broom::glance(modelo.dcl5),
            broom::glance(modelo.dcl6)) %>%
  dplyr::mutate(Modelo = c("A * B + fila + columna + fila/A",
                           "A + B + fila + columna + rep/A",
                           "A * B + fila + fila/A",
                           "A + B + fila + rep/A",
                           "A * B + columna + fila/A",
                           "A + B + columna + rep/A")) %>%
  dplyr::select(Modelo, AIC, BIC) %>%
  dplyr::arrange(BIC) %>%
  dplyr::mutate(Mérito = 1:n()) %>%
  dplyr::relocate(Mérito, Modelo) %>%
  gt()
Mérito Modelo AIC BIC
1 A * B + fila + fila/A 42.32336 46.68752
2 A * B + fila + columna + fila/A 44.32336 49.17243
3 A * B + columna + fila/A 44.32336 49.17243
4 A + B + fila + rep/A 76.35013 79.74448
5 A + B + fila + columna + rep/A 75.73423 80.09839
6 A + B + columna + rep/A 75.73423 80.09839

Definición del modelo


modelo.dcl <- lm(PESO ~ row + FA * FB + row/FA, data = data)

\[Y_i = \beta_0 + \beta_1*F_{II} + \beta_2*A_2 + \beta_3*B_2 + \beta_4*B_3 + \beta_5*A_2*F_{II} + \beta_6*A_2*_B2 + \beta_7*A_2*_B3 + \epsilon_i\]

\[\hat{Y}_i = \beta_0 + \beta_1*F_{II} + \beta_2*A_2 + \beta_3*B_2 + \beta_4*B_3 + \beta_5*A_2*F_{II} + \beta_6*A_2*_B2 + \beta_7*A_2*_B3\]

summary(modelo.dcl)

Call:
lm(formula = PESO ~ row + FA * FB + row/FA, data = data)

Residuals:
      1       2       3       4       5       6       7       8       9      10 
-0.5000  1.0000 -0.5000 -0.6667 -0.1667  0.8333 -1.0000  0.5000  0.5000  0.6667 
     11      12 
-0.8333  0.1667 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.017e+01  9.428e-01  10.783 0.000419 ***
row2         6.667e-01  9.428e-01   0.707 0.518519    
FAA2         6.833e+00  1.333e+00   5.125 0.006862 ** 
FBB2         6.500e+00  1.155e+00   5.629 0.004899 ** 
FBB3         9.000e+00  1.155e+00   7.794 0.001462 ** 
FAA2:FBB2    6.527e-15  1.633e+00   0.000 1.000000    
FAA2:FBB3   -1.350e+01  1.633e+00  -8.267 0.001168 ** 
row2:FAA2   -6.667e-01  1.333e+00  -0.500 0.643330    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.155 on 4 degrees of freedom
Multiple R-squared:  0.9765,    Adjusted R-squared:  0.9353 
F-statistic: 23.71 on 7 and 4 DF,  p-value: 0.004191

Verificación visual de los supuestos del modelo


performance::check_model(modelo.dcl)
ggResidpanel::resid_panel(modelo.dcl)
influence.measures(modelo.dcl)
Influence measures of
     lm(formula = PESO ~ row + FA * FB + row/FA, data = data) :

      dfb.1_  dfb.row2 dfb.FAA2  dfb.FBB2  dfb.FBB3 dfb.FAA2.FBB2 dfb.FAA2.FBB3
1   2.98e-16 -1.67e-16  -0.1752 -2.46e-16 -1.62e-16     -4.29e-01      1.46e-16
2   1.00e-16 -2.00e-16   1.9640  1.42e-16 -4.09e-16     -1.20e+00     -1.20e+00
3  -4.76e-17  9.53e-17  -0.1752 -1.16e-16 -1.91e-16      2.04e-16     -4.29e-01
4  -3.54e-01  7.07e-01   0.2500 -8.66e-01 -2.87e-16      6.12e-01      2.28e-16
5  -7.72e-02  1.54e-01   0.0546  7.71e-17 -1.89e-01     -8.18e-17      1.34e-01
6   1.96e+00 -9.81e-01  -1.3868 -1.20e+00 -1.20e+00      8.49e-01      8.49e-01
7   3.00e-16 -6.68e-17  -0.9820  2.35e-16  8.35e-18      1.20e+00      1.20e+00
8  -1.67e-16  9.53e-17  -0.1752  8.57e-17  4.76e-17     -2.92e-17      4.29e-01
9   2.74e-16 -2.14e-16  -0.1752 -1.45e-16 -4.29e-17      4.29e-01      7.63e-17
10 -3.54e-01  7.07e-01   0.2500  8.66e-01 -2.45e-16     -6.12e-01      2.21e-16
11 -9.81e-01 -9.81e-01   0.6934  1.20e+00  1.20e+00     -8.49e-01     -8.49e-01
12 -7.72e-02  1.54e-01   0.0546 -3.85e-17  1.89e-01      0.00e+00     -1.34e-01
   dfb.r2.F  dffit   cov.r cook.d   hat inf
1     0.350 -0.991  8.9144 0.1406 0.667   *
2    -0.982  2.777  0.0402 0.5625 0.667   *
3     0.350 -0.991  8.9144 0.1406 0.667   *
4    -0.500 -1.414  3.0000 0.2500 0.667    
5    -0.109 -0.309 26.4190 0.0156 0.667   *
6     0.693  1.961  0.5698 0.3906 0.667   *
7    -0.982 -2.777  0.0402 0.5625 0.667   *
8     0.350  0.991  8.9144 0.1406 0.667   *
9     0.350  0.991  8.9144 0.1406 0.667   *
10   -0.500  1.414  3.0000 0.2500 0.667    
11    0.693 -1.961  0.5698 0.3906 0.667   *
12   -0.109  0.309 26.4190 0.0156 0.667   *
influenceIndexPlot(modelo.dcl)

Cumplimiento de supuestos del modelo lineal general


Independencia de residuos

\(H_0: \text{Los residuos del peso son completamente aleatorios e independientes}\)

\(H_1: \text{Los residuos del peso no son completamente aleatorios e independientes}\)

durbinWatsonTest(modelo.dcl,
                 reps = 5000,
                 max.lag = 5)
 lag Autocorrelation D-W Statistic p-value
   1      -0.4010417     2.7500000  0.3804
   2      -0.1458333     1.9218750  0.8564
   3      -0.0468750     1.5937500  0.8644
   4       0.4635417     0.4427083  0.0100
   5      -0.5572917     2.4322917  0.0560
 Alternative hypothesis: rho[lag] != 0
dwtest(modelo.dcl, alternative = "two.sided")

    Durbin-Watson test

data:  modelo.dcl
DW = 2.75, p-value = 0.3847
alternative hypothesis: true autocorrelation is not 0

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los residuos del peso son completamente aleatorios e independientes.

Normalidad de residuos

\(H_0: \text{La distribución de los residuos del peso es similar a la función normal}\)

\(H_1: \text{La distribución de los residuos del peso es similar a la función normal}\)

shapiro.test(rstudent(modelo.dcl))

    Shapiro-Wilk normality test

data:  rstudent(modelo.dcl)
W = 0.97736, p-value = 0.9709
ad.test(rstudent(modelo.dcl))

    Anderson-Darling normality test

data:  rstudent(modelo.dcl)
A = 0.16739, p-value = 0.9154
lillie.test(rstudent(modelo.dcl))

    Lilliefors (Kolmogorov-Smirnov) normality test

data:  rstudent(modelo.dcl)
D = 0.1384, p-value = 0.7587
ks.test(rstudent(modelo.dcl), "pnorm",
        alternative = "two.sided")

    Exact one-sample Kolmogorov-Smirnov test

data:  rstudent(modelo.dcl)
D = 0.17491, p-value = 0.7975
alternative hypothesis: two-sided
cvm.test(rstudent(modelo.dcl))

    Cramer-von Mises normality test

data:  rstudent(modelo.dcl)
W = 0.028196, p-value = 0.8558
pearson.test(rstudent(modelo.dcl))

    Pearson chi-square normality test

data:  rstudent(modelo.dcl)
P = 2, p-value = 0.5724
sf.test(rstudent(modelo.dcl))

    Shapiro-Francia normality test

data:  rstudent(modelo.dcl)
W = 0.98564, p-value = 0.9892

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la distribución de los residuos del peso es similar a la función normal o gaussiana.

Homocedasticidad

\(H_0\): La varianza del peso es constante con respecto a los valores ajustados del peso

\(H_1\): La varianza del peso no es constante con respecto a los valores ajustados del peso

ncvTest(modelo.dcl)
Non-constant Variance Score Test 
Variance formula: ~ fitted.values 
Chisquare = 0.427099, Df = 1, p = 0.51342
bptest(modelo.dcl)

    studentized Breusch-Pagan test

data:  modelo.dcl
BP = 12, df = 7, p-value = 0.1006
bptest(modelo.dcl, studentize = F)

    Breusch-Pagan test

data:  modelo.dcl
BP = 3.1406, df = 7, p-value = 0.8717
olsrr::ols_test_breusch_pagan(modelo.dcl)

 Breusch Pagan Test for Heteroskedasticity
 -----------------------------------------
 Ho: the variance is constant            
 Ha: the variance is not constant        

              Data               
 --------------------------------
 Response : PESO 
 Variables: fitted values of PESO 

        Test Summary         
 ----------------------------
 DF            =    1 
 Chi2          =    0.427099 
 Prob > Chi2   =    0.5134159 

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la varianza del peso es constante con respecto a los valores ajustados del peso.

Recomendación. Debido a que se cumple con el supuesto de homocedasticidad, para evaluar los efectos de los tratamientos con respecto al peso, se debe proceder a realizar el análisis de varianza.

Estadísticas globales

modelo.dcl %>% gvlma()

Call:
lm(formula = PESO ~ row + FA * FB + row/FA, data = data)

Coefficients:
(Intercept)         row2         FAA2         FBB2         FBB3    FAA2:FBB2  
  1.017e+01    6.667e-01    6.833e+00    6.500e+00    9.000e+00    6.527e-15  
  FAA2:FBB3    row2:FAA2  
 -1.350e+01   -6.667e-01  


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = .) 

                       Value p-value                Decision
Global Stat        4.702e+00 0.31921 Assumptions acceptable.
Skewness           2.395e-32 1.00000 Assumptions acceptable.
Kurtosis           1.090e+00 0.29644 Assumptions acceptable.
Link Function      3.547e+00 0.05964 Assumptions acceptable.
Heteroscedasticity 6.503e-02 0.79872 Assumptions acceptable.

Análisis de varianza

\[Y_{ijk} = \mu + \tau_{i} + \gamma_{k} + \text{Error}(\tau\gamma)_{ik} + \beta_{j} + (\tau\beta)_{ij} + \epsilon_{ijk}\]

\[\hat{Y}_{ijk} = \mu + \tau_{i} + \gamma_{k} + \text{Error}(\tau\gamma)_{ik} + \beta_{j} + (\tau\beta)_{ij} \]

Dónde:

\(Y_{ijk}\) = Valor observado de la variable respuesta.

\(\hat{Y}_{ijk}\) = Valor ajustado de la variable respuesta.

\(\mu\) = Promedio observado de la variable respuesta.

\(\tau_{i}\) = Efecto del i-ésimo nivel del factor A.

\(\gamma_{k}\) = Efecto del k-ésimo nivel del factor Fila.

\(\text{Error}(\tau\text{rep})_{ik}\) = Residuo observado del modelo a nivel de parcelas principales.

\(\beta_{j}\) = Efecto del j-ésimo nivel del factor B.

\((\tau\beta)_{ij}\) = Efecto de interacción del factor A x factor B dentro de los niveles ij.

\(\epsilon_{ijk}\) = Residuo observado del modelo a nivel de subparcelas.

Pruebas de hipótesis

Para el factor A (Variedad):

\(H_0: \tau_{A1} = \tau_{A2} = 0\)

\(H_1: \text{En al menos un nivel del factor A el } \tau \text{ es diferente a los demás.}\)

\(H_1: \tau_i \neq 0\text{; en al menos un nivel del factor A.}\)

Para el factor B (Densidad):

\(H_0: \beta_{B1} = \beta_{B2} = \beta_{B3} = 0\)

\(H_1: \text{En al menos un nivel del factor B el } \beta \text{ es diferente a los demás.}\)

\(H_1: \beta_j \neq 0\text{; en al menos un nivel del factor B.}\)

Para la interacción entre factor A y factor B:

\(H_0: (\tau\beta)_{A1B1} = (\tau\beta)_{A1B2} = (\tau\beta)_{A1B3} = (\tau\beta)_{A2B1} = (\tau\beta)_{A2B2} = (\tau\beta)_{A2B3} = 0\)

\(H_1: \text{En al menos una interacción entre el factor A y el factor B el } (\tau\beta) \text{ es diferente a los demás.}\)

\(H_1: (\tau\beta)_{ij} \neq 0\text{; en al menos una interacción entre el factor A y el factor B.}\)

Precaución

  • Si se ignora el diseño experimental, se obtienen los siguientes resultados, incorrectos. Observe que los grados de libertad del error es mayor, lo que facilita la detección de diferencias que en realidad no existen.
anova(modelo.dcl, test = "F")
Analysis of Variance Table

Response: PESO
          Df  Sum Sq Mean Sq F value   Pr(>F)   
row        1   0.333   0.333   0.250 0.643330   
FA         1  12.000  12.000   9.000 0.039942 * 
FB         2  87.167  43.583  32.688 0.003324 **
FA:FB      2 121.500  60.750  45.562 0.001768 **
row:FA     1   0.333   0.333   0.250 0.643330   
Residuals  4   5.333   1.333                    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Importante

Necesitamos especificar correctamente el término de error para el factor A. Debe tenerse en cuenta que la forma del Error es “Error(A:parcelagrande)” en el caso de efectos aleatorios o “Error(A:bloque)” para el caso de efectos fijos y puede cambiar dependiendo de la disposición de los datos. La clave es conocer los grados de libertad correcto para saber que se obtienen los resultados correctos.

aov(PESO ~ FA * FB + row + Error(row/FA), data = data) -> aov.dcl
summary(aov.dcl)

Error: row
    Df Sum Sq Mean Sq
row  1 0.3333  0.3333

Error: row:FA
          Df Sum Sq Mean Sq F value Pr(>F)
FA         1 12.000  12.000      36  0.105
Residuals  1  0.333   0.333               

Error: Within
          Df Sum Sq Mean Sq F value  Pr(>F)   
FB         2  87.17   43.58   32.69 0.00332 **
FA:FB      2 121.50   60.75   45.56 0.00177 **
Residuals  4   5.33    1.33                   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
broom::tidy(aov.dcl)
# A tibble: 6 × 7
  stratum term         df   sumsq meansq statistic  p.value
  <chr>   <chr>     <dbl>   <dbl>  <dbl>     <dbl>    <dbl>
1 row     row           1   0.333  0.333      NA   NA      
2 row:FA  FA            1  12.0   12.0        36.0  0.105  
3 row:FA  Residuals     1   0.333  0.333      NA   NA      
4 Within  FB            2  87.2   43.6        32.7  0.00332
5 Within  FA:FB         2 122.    60.8        45.6  0.00177
6 Within  Residuals     4   5.33   1.33       NA   NA      

Valor de la tabla de F para el factor A con una significancia de 0.05.

qf(0.95, 1, 1)
[1] 161.4476

Valor de la tabla de F para el factor B con una significancia de 0.05.

qf(0.95, 2, 4)
[1] 6.944272

Valor de la tabla de F para la interacción A:B con una significancia de 0.05.

qf(0.95, 2, 4)
[1] 6.944272
shadeDist(qf(0.95, 2, 4), "df",2, 4, lower.tail = F)

Conclusión.

Con respecto al Factor A: A un nivel de significancia de 0.05, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los niveles del factor A tienen un efecto sobre el rendimiento estadísticamente similar a 0.

Con respecto al Factor B: A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos un nivel del factor B tienen un efecto sobre el rendimiento estadísticamente diferente a 0.

Con respecto a la interacción entre el Factor A y Factor B: A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos una interacción entre un nivel del factor A y un nivel del factor B existe un efecto de antagonismo o sinergismo sobre el rendimiento.

agricolae::cv.model(modelo.dcl)
[1] 6.928203
cv.a <- sqrt(get_mse_ea_spplot(object = aov.dcl))*100/mean(data$PESO)
cv.a
[1] 3.464102
cv.b <- sqrt(dvmisc::get_mse(modelo.dcl))*100/mean(data$PESO)
cv.b
[1] 6.928203

Comparaciones de medias para los efectos principales del Factor A

data %>% with(LSD.test(
  PESO, # Cambiar según nombre de variable respuesta
  FA, # Cambiar según nombre de variable independiente
  DFerror = get_df_ea_spplot(aov.dcl), 
  MSerror = get_mse_ea_spplot(aov.dcl),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: PESO ~ FA

LSD t Test for PESO 

Mean Square Error:  0.3333333 

FA,  means and individual ( 95 %) CI

       PESO      std r      LCL      UCL Min Max
A1 15.66667 4.226898 6 12.67179 18.66155  10  20
A2 17.66667 5.006662 6 14.67179 20.66155  12  24

Alpha: 0.05 ; DF Error: 1
Critical Value of t: 12.7062 

least Significant Difference: 4.235402 

Treatments with the same letter are not significantly different.

       PESO groups
A2 17.66667      a
A1 15.66667      a

Comparaciones de medias para los efectos principales del Factor B

data %>% with(LSD.test(
  PESO, # Cambiar según nombre de variable respuesta
  FB, # Cambiar según nombre de variable independiente
  DFerror = df.residual(modelo.dcl), 
  MSerror = dvmisc::get_mse(modelo.dcl),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: PESO ~ FB

LSD t Test for PESO 

Mean Square Error:  1.333333 

FB,  means and individual ( 95 %) CI

    PESO      std r      LCL      UCL Min Max
B1 13.75 3.862210 4 12.14702 15.35298  10  18
B2 20.25 3.862210 4 18.64702 21.85298  16  24
B3 16.00 4.082483 4 14.39702 17.60298  12  20

Alpha: 0.05 ; DF Error: 4
Critical Value of t: 2.776445 

least Significant Difference: 2.266958 

Treatments with the same letter are not significantly different.

    PESO groups
B2 20.25      a
B3 16.00      b
B1 13.75      b

Precaución

Si el análisis de varianza arroja que los niveles de un factor son estadísticamente similares entre sí, entonces no es necesario realizar una prueba de comparación de medias y por ende todos estos niveles pertenecen a un mismo grupo de significancia “a”.

Comparaciones de medias para las interacciones

Para los niveles del factor A dentro del nivel B1:

  • A1 vs A2:

\(H_0: \mu_{A1} - \mu_{A2} = 0\)

\(H_1: \mu_{A1} - \mu_{A2} \neq 0\)

Para los niveles del factor B dentro del nivel A1:

  • B1 vs B2:

\(H_0: \mu_{B1} - \mu_{B2} = 0\)

\(H_1: \mu_{B1} - \mu_{B2} \neq 0\)

  • B1 vs B3:

\(H_0: \mu_{B1} - \mu_{B3} = 0\)

\(H_1: \mu_{B1} - \mu_{B3} \neq 0\)

  • B2 vs B3:

\(H_0: \mu_{B2} - \mu_{B3} = 0\)

\(H_1: \mu_{B2} - \mu_{B3} \neq 0\)

NOTA: Repetir este proceso para cada nivel de A y cada nivel de B.

Análisis de varianza para interacción de dos factores con el paquete phia

Comparación de los niveles de B dentro de cada nivel de A

phia::testInteractions(modelo.dcl,
                       fixed = "FA",
                       across = "FB",
                       adjustment = "none")
F Test: 
P-value adjustment method: none
           FB1  FB2 Df Sum of Sq      F   Pr(>F)   
A1        -9.0 -2.5  2    86.333 32.375 0.003385 **
A2         4.5 11.0  2   122.333 45.875 0.001745 **
Residuals            4     5.333                   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Comparación de los niveles de A dentro de cada nivel de B

phia::testInteractions(modelo.dcl,
                       fixed = "FB",
                       across = "FA",
                       adjustment = "none")
F Test: 
P-value adjustment method: none
          Value Df Sum of Sq      F   Pr(>F)   
B1         -6.5  1    42.250 31.688 0.004899 **
B2         -6.5  1    42.250 31.688 0.004899 **
B3          7.0  1    49.000 36.750 0.003738 **
Residuals        4     5.333                   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Plot de interacciones

phia::interactionMeans(model = modelo.dcl,
                       factors = c("FA","FB")) %>%
  plot()

Comparaciones de medias de los niveles de B dentro de cada nivel de A

FA_A1 <- data %>% filter(FA=="A1")
FA_A2 <- data %>% filter(FA=="A2")

fcomp1 <- function(x){
  comp <- LSD.test(x$PESO, # Cambiar según nombre de variable respuesta
                   x$FB, # Cambiar según nombre de variable independiente
                   DFerror = df.residual(modelo.dcl), 
                   MSerror = dvmisc::get_mse(modelo.dcl),
                   alpha = 0.05,
                   group=TRUE,
                   main = NULL,
                   console=FALSE)
  return(comp[[5]] %>%
           rename("Peso" = "x$PESO") # Cambiar según nombre de variable respuesta
         )
}

Comparaciones de los niveles de B dentro del nivel A1

fcomp1(FA_A1)
   Peso groups
B3 19.5      a
B2 17.0      a
B1 10.5      b

Comparaciones de los niveles de B dentro del nivel A2

fcomp1(FA_A2)
   Peso groups
B2 23.5      a
B1 17.0      b
B3 12.5      c

Comparaciones de medias de los niveles de B dentro de cada nivel de A

FB_B1 <- data %>% filter(FB=="B1")
FB_B2 <- data %>% filter(FB=="B2")
FB_B3 <- data %>% filter(FB=="B3")

fcomp2 <- function(x){
  comp <- LSD.test(x$PESO, # Cambiar según nombre de variable respuesta
                   x$FA, # Cambiar según nombre de variable independiente
                   DFerror = df.residual(modelo.dcl), 
                   MSerror = dvmisc::get_mse(modelo.dcl),
                   alpha = 0.05,
                   group=TRUE,
                   main = NULL,
                   console=FALSE)
  return(comp[[5]] %>%
           rename("Peso" = "x$PESO") # Cambiar según nombre de variable respuesta
         )
}

Comparaciones de los niveles de A dentro del nivel B1

fcomp2(FB_B1)
   Peso groups
A2 17.0      a
A1 10.5      b

Comparaciones de los niveles de A dentro del nivel B2

fcomp2(FB_B2)
   Peso groups
A2 23.5      a
A1 17.0      b

Comparaciones de los niveles de A dentro del nivel B3

fcomp2(FB_B3)
   Peso groups
A1 19.5      a
A2 12.5      b

Diseño de bloques completos al azar en arreglo de parcelas sub-divididas

Planeamiento


Crear un libro de campo con el paquete agricolae


FA <- c("A1","A2","A3")
FB <- c("B1","B2")
FC <- c("C1","C2")

r <- 5

salida <- agricolae::design.split(trt1 = FA,
                                  trt2 = FB,
                                  r = r,
                                  design = "rcbd",
                                  serie = 3,
                                  seed = 123,
                                  kinds = "Super-Duper",
                                  randomization = TRUE)
book <- salida$book

Sketch de parcelas grandes

p <- book$FA[seq(1,nrow(book),2)]
print(t(matrix(p,c(length(FA),r))))
     [,1] [,2] [,3]
[1,] "A3" "A1" "A2"
[2,] "A3" "A1" "A2"
[3,] "A2" "A1" "A3"
[4,] "A2" "A3" "A1"
[5,] "A2" "A1" "A3"
p <- book$plots[seq(1,nrow(book),2)]
print(t(matrix(p,c(length(FA),r))))
     [,1] [,2] [,3]
[1,] 1001 1002 1003
[2,] 1004 1005 1006
[3,] 1007 1008 1009
[4,] 1010 1011 1012
[5,] 1013 1014 1015

Sketch de parcelas medianas

q <- NULL
for(i in 1:length(p))
  q <- c(q,paste(book$FB[2*(i-1)+1],book$FB[2*(i-1)+2]))
print(t(matrix(q,c(length(FA),r))))
     [,1]    [,2]    [,3]   
[1,] "B2 B1" "B1 B2" "B1 B2"
[2,] "B1 B2" "B1 B2" "B1 B2"
[3,] "B1 B2" "B2 B1" "B2 B1"
[4,] "B1 B2" "B2 B1" "B2 B1"
[5,] "B2 B1" "B1 B2" "B1 B2"
concatenar_n_ssplot <- function(vector, n) {
  s <- NULL
  for(i in seq(from=1, to=length(vector), by=n)) {
    indices <- i:(i+n-1)
    grupo <- vector[indices]
    combinacion <- paste(grupo, collapse=" ")
    s <- c(s, combinacion)
  }
  return(s)
}

q <- concatenar_n_ssplot(vector = book$FB,
      # n es el número de parcelas medianas por parcela principal
                         n = 2)


print(t(matrix(q,c(length(FA),r))))
     [,1]    [,2]    [,3]   
[1,] "B2 B1" "B1 B2" "B1 B2"
[2,] "B1 B2" "B1 B2" "B1 B2"
[3,] "B1 B2" "B2 B1" "B2 B1"
[4,] "B1 B2" "B2 B1" "B2 B1"
[5,] "B2 B1" "B1 B2" "B1 B2"

Parcelas chicas

rpc <- r*length(FA)*length(FB)

dbca.des <- agricolae::design.rcbd(trt = FC,
                                   r = rpc,
                                   serie = 3,
                                   seed = 123,
                                   kinds = "Super-Duper",
                                   first = T,
                                   continue = T,
                                   randomization = T)
bookssp <- dbca.des$book

prebook <- book[rep(seq_len(nrow(book)), each = length(FC)), ]
prebook
     plots splots block FA FB
1     1001      1     1 A3 B2
1.1   1001      1     1 A3 B2
2     1001      2     1 A3 B1
2.1   1001      2     1 A3 B1
3     1002      1     1 A1 B1
3.1   1002      1     1 A1 B1
4     1002      2     1 A1 B2
4.1   1002      2     1 A1 B2
5     1003      1     1 A2 B1
5.1   1003      1     1 A2 B1
6     1003      2     1 A2 B2
6.1   1003      2     1 A2 B2
7     1004      1     2 A3 B1
7.1   1004      1     2 A3 B1
8     1004      2     2 A3 B2
8.1   1004      2     2 A3 B2
9     1005      1     2 A1 B1
9.1   1005      1     2 A1 B1
10    1005      2     2 A1 B2
10.1  1005      2     2 A1 B2
11    1006      1     2 A2 B1
11.1  1006      1     2 A2 B1
12    1006      2     2 A2 B2
12.1  1006      2     2 A2 B2
13    1007      1     3 A2 B1
13.1  1007      1     3 A2 B1
14    1007      2     3 A2 B2
14.1  1007      2     3 A2 B2
15    1008      1     3 A1 B2
15.1  1008      1     3 A1 B2
16    1008      2     3 A1 B1
16.1  1008      2     3 A1 B1
17    1009      1     3 A3 B2
17.1  1009      1     3 A3 B2
18    1009      2     3 A3 B1
18.1  1009      2     3 A3 B1
19    1010      1     4 A2 B1
19.1  1010      1     4 A2 B1
20    1010      2     4 A2 B2
20.1  1010      2     4 A2 B2
21    1011      1     4 A3 B2
21.1  1011      1     4 A3 B2
22    1011      2     4 A3 B1
22.1  1011      2     4 A3 B1
23    1012      1     4 A1 B2
23.1  1012      1     4 A1 B2
24    1012      2     4 A1 B1
24.1  1012      2     4 A1 B1
25    1013      1     5 A2 B2
25.1  1013      1     5 A2 B2
26    1013      2     5 A2 B1
26.1  1013      2     5 A2 B1
27    1014      1     5 A1 B1
27.1  1014      1     5 A1 B1
28    1014      2     5 A1 B2
28.1  1014      2     5 A1 B2
29    1015      1     5 A3 B1
29.1  1015      1     5 A3 B1
30    1015      2     5 A3 B2
30.1  1015      2     5 A3 B2
splots <- data.frame(splots = rep(1:nrow(book), each = length(FC)))
splots
   splots
1       1
2       1
3       2
4       2
5       3
6       3
7       4
8       4
9       5
10      5
11      6
12      6
13      7
14      7
15      8
16      8
17      9
18      9
19     10
20     10
21     11
22     11
23     12
24     12
25     13
26     13
27     14
28     14
29     15
30     15
31     16
32     16
33     17
34     17
35     18
36     18
37     19
38     19
39     20
40     20
41     21
42     21
43     22
44     22
45     23
46     23
47     24
48     24
49     25
50     25
51     26
52     26
53     27
54     27
55     28
56     28
57     29
58     29
59     30
60     30
total_col <- length(levels(FA)) * length(levels(FB)) * length(levels(FC))
bookssp <- data.frame(plots = prebook$plots,
                      splots = splots,
                      ssplots = as.factor(1:length(FC)),
                      block = as.factor(prebook$block),
                      FA = as.factor(prebook$FA),
                      FB = as.factor(prebook$FB),
                      FC = as.factor(bookssp$FC),
                      col = factor(rep(1:total_col, r)))%>% 
  mutate(row = rev(as.factor(as.integer(block))))
s <- bookssp$FC
print(t(matrix(s,c(length(FA)*length(FB)*length(FC),r))))
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
[1,] "C1" "C2" "C1" "C2" "C1" "C2" "C2" "C1" "C1" "C2"  "C2"  "C1" 
[2,] "C2" "C1" "C2" "C1" "C2" "C1" "C1" "C2" "C2" "C1"  "C1"  "C2" 
[3,] "C2" "C1" "C2" "C1" "C2" "C1" "C1" "C2" "C1" "C2"  "C2"  "C1" 
[4,] "C2" "C1" "C2" "C1" "C1" "C2" "C1" "C2" "C1" "C2"  "C2"  "C1" 
[5,] "C1" "C2" "C1" "C2" "C2" "C1" "C1" "C2" "C1" "C2"  "C2"  "C1" 
s <- concatenar_n_ssplot(vector = bookssp$FC,
# n es el número de parcelas chicas por parcela principal
                         n = 4)
print(t(matrix(s,c(length(FA),r))))
     [,1]          [,2]          [,3]         
[1,] "C1 C2 C1 C2" "C1 C2 C2 C1" "C1 C2 C2 C1"
[2,] "C2 C1 C2 C1" "C2 C1 C1 C2" "C2 C1 C1 C2"
[3,] "C2 C1 C2 C1" "C2 C1 C1 C2" "C1 C2 C2 C1"
[4,] "C2 C1 C2 C1" "C1 C2 C1 C2" "C1 C2 C2 C1"
[5,] "C1 C2 C1 C2" "C2 C1 C1 C2" "C1 C2 C2 C1"

Matriz final

plots <- paste(bookssp$FA,bookssp$FB,bookssp$FC)
print(matrix(plots, byrow = T, ncol = 12))
     [,1]       [,2]       [,3]       [,4]       [,5]       [,6]      
[1,] "A3 B2 C1" "A3 B2 C2" "A3 B1 C1" "A3 B1 C2" "A1 B1 C1" "A1 B1 C2"
[2,] "A3 B1 C2" "A3 B1 C1" "A3 B2 C2" "A3 B2 C1" "A1 B1 C2" "A1 B1 C1"
[3,] "A2 B1 C2" "A2 B1 C1" "A2 B2 C2" "A2 B2 C1" "A1 B2 C2" "A1 B2 C1"
[4,] "A2 B1 C2" "A2 B1 C1" "A2 B2 C2" "A2 B2 C1" "A3 B2 C1" "A3 B2 C2"
[5,] "A2 B2 C1" "A2 B2 C2" "A2 B1 C1" "A2 B1 C2" "A1 B1 C2" "A1 B1 C1"
     [,7]       [,8]       [,9]       [,10]      [,11]      [,12]     
[1,] "A1 B2 C2" "A1 B2 C1" "A2 B1 C1" "A2 B1 C2" "A2 B2 C2" "A2 B2 C1"
[2,] "A1 B2 C1" "A1 B2 C2" "A2 B1 C2" "A2 B1 C1" "A2 B2 C1" "A2 B2 C2"
[3,] "A1 B1 C1" "A1 B1 C2" "A3 B2 C1" "A3 B2 C2" "A3 B1 C2" "A3 B1 C1"
[4,] "A3 B1 C1" "A3 B1 C2" "A1 B2 C1" "A1 B2 C2" "A1 B1 C2" "A1 B1 C1"
[5,] "A1 B2 C1" "A1 B2 C2" "A3 B1 C1" "A3 B1 C2" "A3 B2 C2" "A3 B2 C1"
bookssp %>% 
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)

Guardar el libro generado

write.table(salida$book,
            "books/rcbdspspplot.txt",
            row.names = FALSE,
            sep = "\t")

write.xlsx(salida$book,
           "books/rcbdspspplot.xlsx",
           sheetName = "book",
           append = FALSE,
           row.names = FALSE)

Guardar el libro de campo generado

write.table(salida %>% zigzag(),
            "books/rcbdspspplot.txt",
            row.names = FALSE,
            sep = "\t")

write.xlsx(salida %>% zigzag(),
           "books/rcbdspspplot.xlsx",
           sheetName = "book",
           append = FALSE,
           row.names = FALSE)
ggplot(bookssp,
       aes(col, y = row)) +
  geom_tile(aes(fill = FA)) + 
  theme_bw() + 
  theme(line = element_blank()) + 
  geom_text(aes(label = plots), colour = "black")
ggplot(bookssp,
       aes(col, y = row)) +
  geom_tile(aes(fill = FB)) + 
  theme_bw() + 
  theme(line = element_blank()) + 
  geom_text(aes(label = plots), colour = "black")
ggplot(bookssp,
       aes(col, y = row)) +
  geom_tile(aes(fill = FC)) + 
  theme_bw() + 
  theme(line = element_blank()) + 
  geom_text(aes(label = plots), colour = "black")

Análisis de DBCA en arreglo factorial de parcelas sub-divididas


Importación de datos


archivos <- list.files(pattern = "datos split split plot.xlsx", 
                       full.names = TRUE,
                       recursive = TRUE)

# Importación
data <- readxl::read_xlsx(archivos,
                           sheet = "ej1")

# Preprocesamiento

data <- data %>%
  mutate_if(is.character, factor) %>%
  mutate(bloque = factor(bloque),
         nitrogeno = factor(nitrogeno),
         variedad = factor(variedad))
attach(data)

Creación del modelo lineal


modelo.dbca1 <- lm(rdto ~ nitrogeno * manejo * variedad + bloque/nitrogeno/manejo + bloque, data = data)
modelo.dbca2 <- lm(rdto ~ nitrogeno * manejo + variedad + bloque/nitrogeno/manejo + bloque, data = data)
modelo.dbca3 <- lm(rdto ~ nitrogeno + manejo * variedad + bloque/nitrogeno/manejo + bloque, data = data)
modelo.dbca4 <- lm(rdto ~ nitrogeno * variedad + manejo + bloque/nitrogeno/manejo + bloque, data = data)
modelo.dbca5 <- lm(rdto ~ nitrogeno + manejo + variedad + bloque/nitrogeno/manejo + bloque, data = data)
broom::glance(modelo.dbca1) %>%
  bind_rows(broom::glance(modelo.dbca2),
            broom::glance(modelo.dbca3),
            broom::glance(modelo.dbca4),
            broom::glance(modelo.dbca5)) %>%
  dplyr::mutate(Modelo = c("A * B * C + bloque + bloque/A/B",
                           "A * B + C + bloque + bloque/A/B",
                           "A + B * C + bloque + bloque/A/B",
                           "A * C + B + bloque + bloque/A/B",
                           "A + B + C + bloque + bloque/A/B")) %>%
  dplyr::select(Modelo, AIC, BIC) %>%
  dplyr::arrange(BIC) %>%
  dplyr::mutate(Mérito = 1:n()) %>%
  dplyr::relocate(Mérito, Modelo) %>%
  gt()
Mérito Modelo AIC BIC
1 A * C + B + bloque + bloque/A/B 321.4056 484.1010
2 A + B + C + bloque + bloque/A/B 348.8260 488.2792
3 A * B + C + bloque + bloque/A/B 348.8260 488.2792
4 A + B * C + bloque + bloque/A/B 346.3163 497.3906
5 A * B * C + bloque + bloque/A/B 330.8538 551.6546

Definición del modelo


modelo.dbca <- lm(rdto ~ nitrogeno * variedad + manejo + bloque + bloque/nitrogeno/manejo, data = data)
summary(modelo.dbca)

Call:
lm(formula = rdto ~ nitrogeno * variedad + manejo + bloque + 
    bloque/nitrogeno/manejo, data = data)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.73056 -0.33346 -0.02752  0.37965  1.39748 

Coefficients: (2 not defined because of singularities)
                              Estimate Std. Error t value Pr(>|t|)    
(Intercept)                    4.05374    0.43574   9.303 2.23e-14 ***
nitrogeno50                   -0.34741    0.61623  -0.564 0.574493    
nitrogeno80                    1.23941    0.61623   2.011 0.047664 *  
nitrogeno110                   0.61922    0.61623   1.005 0.317996    
nitrogeno140                   0.22544    0.61623   0.366 0.715447    
variedad2                      0.64978    0.32182   2.019 0.046826 *  
variedad3                      1.96500    0.32182   6.106 3.48e-08 ***
manejom2                       1.10967    0.55740   1.991 0.049919 *  
manejom3                       2.22933    0.55740   4.000 0.000141 ***
bloque2                       -0.08467    0.55740  -0.152 0.879652    
bloque3                       -0.07000    0.55740  -0.126 0.900377    
nitrogeno50:variedad2          0.60278    0.45512   1.324 0.189125    
nitrogeno80:variedad2          0.10389    0.45512   0.228 0.820020    
nitrogeno110:variedad2         0.83011    0.45512   1.824 0.071893 .  
nitrogeno140:variedad2         1.56089    0.45512   3.430 0.000958 ***
nitrogeno50:variedad3          1.15244    0.45512   2.532 0.013292 *  
nitrogeno80:variedad3          0.76389    0.45512   1.678 0.097162 .  
nitrogeno110:variedad3         1.03322    0.45512   2.270 0.025883 *  
nitrogeno140:variedad3         2.29278    0.45512   5.038 2.86e-06 ***
nitrogeno50:bloque2            0.94767    0.78828   1.202 0.232837    
nitrogeno80:bloque2           -0.21133    0.78828  -0.268 0.789318    
nitrogeno110:bloque2           0.26033    0.78828   0.330 0.742072    
nitrogeno140:bloque2           0.24167    0.78828   0.307 0.759965    
nitrogeno50:bloque3            0.65300    0.78828   0.828 0.409919    
nitrogeno80:bloque3            0.14300    0.78828   0.181 0.856507    
nitrogeno110:bloque3          -0.24767    0.78828  -0.314 0.754199    
nitrogeno140:bloque3           0.06233    0.78828   0.079 0.937171    
nitrogeno0:manejom2:bloque1   -0.60033    0.78828  -0.762 0.448556    
nitrogeno50:manejom2:bloque1  -0.08133    0.78828  -0.103 0.918080    
nitrogeno80:manejom2:bloque1  -0.62400    0.78828  -0.792 0.430939    
nitrogeno110:manejom2:bloque1 -0.16633    0.78828  -0.211 0.833418    
nitrogeno140:manejom2:bloque1 -0.38833    0.78828  -0.493 0.623622    
nitrogeno0:manejom3:bloque1   -1.07100    0.78828  -1.359 0.178077    
nitrogeno50:manejom3:bloque1  -0.48300    0.78828  -0.613 0.541797    
nitrogeno80:manejom3:bloque1  -1.25667    0.78828  -1.594 0.114839    
nitrogeno110:manejom3:bloque1 -0.37700    0.78828  -0.478 0.633774    
nitrogeno140:manejom3:bloque1 -1.05433    0.78828  -1.338 0.184848    
nitrogeno0:manejom2:bloque2   -0.73500    0.78828  -0.932 0.353933    
nitrogeno50:manejom2:bloque2  -1.00900    0.78828  -1.280 0.204246    
nitrogeno80:manejom2:bloque2  -0.20467    0.78828  -0.260 0.795812    
nitrogeno110:manejom2:bloque2  0.08700    0.78828   0.110 0.912395    
nitrogeno140:manejom2:bloque2 -0.71233    0.78828  -0.904 0.368894    
nitrogeno0:manejom3:bloque2   -0.59333    0.78828  -0.753 0.453845    
nitrogeno50:manejom3:bloque2  -0.73733    0.78828  -0.935 0.352415    
nitrogeno80:manejom3:bloque2  -0.66733    0.78828  -0.847 0.399763    
nitrogeno110:manejom3:bloque2 -1.08367    0.78828  -1.375 0.173058    
nitrogeno140:manejom3:bloque2 -1.12267    0.78828  -1.424 0.158280    
nitrogeno0:manejom2:bloque3   -1.09000    0.78828  -1.383 0.170589    
nitrogeno50:manejom2:bloque3  -0.96567    0.78828  -1.225 0.224161    
nitrogeno80:manejom2:bloque3  -0.83967    0.78828  -1.065 0.289997    
nitrogeno110:manejom2:bloque3 -0.52867    0.78828  -0.671 0.504372    
nitrogeno140:manejom2:bloque3       NA         NA      NA       NA    
nitrogeno0:manejom3:bloque3   -1.32900    0.78828  -1.686 0.095704 .  
nitrogeno50:manejom3:bloque3  -1.56267    0.78828  -1.982 0.050872 .  
nitrogeno80:manejom3:bloque3  -0.88000    0.78828  -1.116 0.267615    
nitrogeno110:manejom3:bloque3 -0.57700    0.78828  -0.732 0.466326    
nitrogeno140:manejom3:bloque3       NA         NA      NA       NA    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.6827 on 80 degrees of freedom
Multiple R-squared:  0.9002,    Adjusted R-squared:  0.8328 
F-statistic: 13.36 on 54 and 80 DF,  p-value: < 2.2e-16

Verificación visual de los supuestos del modelo


performance::check_model(modelo.dbca)
ggResidpanel::resid_panel(modelo.dbca)
influence.measures(modelo.dbca)
Influence measures of
     lm(formula = rdto ~ nitrogeno * variedad + manejo + bloque +      bloque/nitrogeno/manejo, data = data) :

       dfb.1_  dfb.nt50  dfb.nt80 dfb.nt110 dfb.nt140  dfb.vrd2  dfb.vrd3
1   -1.16e+00  8.24e-01  8.24e-01  8.24e-01  8.24e-01  4.30e-01  4.30e-01
2   -2.31e-01  1.63e-01  1.63e-01  1.63e-01  1.63e-01  4.68e-01  4.68e-01
3   -1.58e-01  1.12e-01  1.12e-01  1.12e-01  1.12e-01  3.22e-01  3.22e-01
4    5.18e-16 -5.78e-01 -4.35e-16 -8.66e-16 -1.40e-15  1.16e-15  1.91e-16
5    7.87e-16 -2.30e-01 -4.05e-16 -5.58e-16  1.08e-15 -8.95e-16 -6.44e-16
6    2.01e-16 -4.45e-02 -1.28e-16 -1.22e-16 -8.95e-17 -8.97e-16 -3.13e-16
7   -1.01e-16  2.22e-16  1.94e-01  2.96e-17 -4.45e-17  2.22e-16  3.81e-16
8   -1.86e-17  1.88e-17 -3.99e-03  1.75e-17  1.38e-17 -9.44e-19  4.13e-18
9   -8.63e-17  4.58e-17 -1.02e-02  5.48e-17  4.37e-17  3.28e-17  3.58e-17
10  -1.60e-15  1.38e-15  1.32e-15 -4.75e-01  1.10e-15  1.21e-16  1.88e-16
11   5.65e-16 -2.23e-16 -4.08e-16 -7.30e-02 -4.63e-16 -1.02e-16  4.36e-18
12   1.02e-16 -2.84e-16 -1.07e-16  6.13e-02 -1.31e-16 -2.26e-16 -2.74e-16
13  -9.39e-16  8.18e-16  9.91e-16  5.90e-16 -1.31e+00  4.20e-16  2.90e-16
14  -2.95e-17  3.14e-18 -4.17e-17  4.16e-17  7.86e-02  1.55e-17  8.15e-17
15   3.44e-17 -5.67e-17 -1.98e-17 -2.96e-17 -4.79e-02  7.67e-18  4.67e-17
16  -3.00e-02  2.12e-02  2.12e-02  2.12e-02  2.12e-02  6.09e-02  6.09e-02
17  -9.33e-03  6.60e-03  6.60e-03  6.60e-03  6.60e-03  1.90e-02  1.90e-02
18   8.85e-02 -6.26e-02 -6.26e-02 -6.26e-02 -6.26e-02 -1.80e-01 -1.80e-01
19   1.34e-16  3.68e-02 -1.12e-16 -1.18e-16 -8.27e-17 -1.24e-16 -6.97e-17
20   1.44e-16  2.80e-02 -1.20e-16 -1.20e-16 -1.04e-16 -5.57e-17 -2.33e-17
21  -8.35e-17 -1.83e-01  1.01e-16  4.85e-16 -9.51e-17  4.00e-16  2.49e-16
22  -1.06e-15  6.06e-16  1.62e-01  9.79e-16  6.04e-16  3.55e-16  3.77e-16
23  -1.99e-17  1.11e-17  4.60e-02 -6.10e-18  7.91e-17 -2.28e-17 -2.14e-17
24  -1.59e-16  6.26e-17  1.11e-01  1.92e-16  7.35e-17 -6.74e-17  6.99e-18
25  -3.04e-18 -2.03e-18  3.73e-18 -1.34e-03  1.11e-18  1.00e-19  2.24e-18
26   2.64e-16 -6.64e-18 -2.14e-16 -6.13e-02 -1.93e-16 -7.38e-17 -1.10e-17
27   8.83e-17 -1.19e-17 -5.58e-17 -2.53e-02 -6.96e-17 -2.28e-17  3.11e-18
28  -3.25e-17  8.65e-18  3.23e-17  2.61e-17 -1.23e-02  5.36e-18  1.36e-17
29   3.61e-17  5.25e-17 -3.79e-17 -7.43e-17 -1.05e-01  2.96e-17  7.25e-17
30   7.57e-18 -3.35e-18  4.21e-17 -5.48e-18 -3.10e-02  4.25e-18  1.67e-17
31   1.50e-01 -1.06e-01 -1.06e-01 -1.06e-01 -1.06e-01 -3.05e-01 -3.05e-01
32   2.53e-01 -1.79e-01 -1.79e-01 -1.79e-01 -1.79e-01 -5.14e-01 -5.14e-01
33   1.48e-01 -1.05e-01 -1.05e-01 -1.05e-01 -1.05e-01 -3.01e-01 -3.01e-01
34   3.45e-17  9.45e-02 -4.32e-17 -7.19e-17 -3.15e-17 -2.85e-16 -1.36e-16
35   2.34e-16  1.77e-01 -2.39e-16 -3.30e-16 -2.14e-16 -3.98e-16 -2.41e-16
36   2.27e-16  2.26e-01 -1.60e-16 -3.08e-16 -1.43e-16 -4.66e-16 -2.22e-16
37   2.75e-16 -1.88e-16 -1.94e-01 -1.58e-16 -7.66e-17 -2.81e-17 -1.26e-16
38   2.27e-18 -1.87e-17 -6.63e-02 -3.60e-19  5.14e-17 -2.39e-17  2.09e-18
39  -7.70e-17  3.89e-17 -8.04e-02  1.05e-16  1.19e-16 -1.08e-18 -5.22e-17
40  -2.13e-17  2.57e-16  1.71e-17  1.03e-01  6.56e-17  3.09e-17 -1.28e-16
41  -9.97e-17 -3.88e-17  4.48e-17  8.27e-02  3.29e-18  4.67e-17 -1.92e-17
42  -1.43e-18 -4.34e-19  5.66e-19  6.79e-04  7.04e-19  8.29e-19  3.61e-19
43  -2.21e-15 -5.35e-16  5.42e-16  1.80e-15  8.22e-02 -5.51e-17 -6.28e-16
44   9.49e-16  1.01e-15 -5.69e-16 -9.50e-16  1.04e-01  4.04e-16  4.52e-16
45   3.08e-15 -2.39e-16  4.92e-17 -1.75e-15  1.65e-01 -5.43e-16  3.14e-16
46   1.67e+00 -1.18e+00 -1.18e+00 -1.18e+00 -1.18e+00  8.47e-01  1.01e-14
47   1.67e-02 -1.18e-02 -1.18e-02 -1.18e-02 -1.18e-02 -6.77e-02  4.46e-16
48  -1.03e-01  7.25e-02  7.25e-02  7.25e-02  7.25e-02  4.17e-01 -2.59e-16
49   5.90e-16  5.18e-01 -4.06e-16 -4.30e-16 -3.05e-16 -9.06e-16 -5.06e-16
50   2.18e-16 -3.74e-02 -1.51e-16 -1.06e-16 -1.31e-16 -2.40e-16 -1.47e-16
51  -1.86e-17 -3.14e-02  1.91e-17 -1.51e-17 -5.82e-17 -1.33e-16 -2.17e-16
52  -1.79e-16  7.93e-17 -4.92e-01  3.37e-16  2.29e-16 -3.98e-16 -7.36e-18
53   1.08e-16 -7.76e-17  1.36e-02 -8.31e-17 -7.08e-17 -2.12e-18 -3.53e-17
54   6.35e-17 -4.19e-17  6.70e-03 -4.63e-17 -5.43e-17 -3.01e-18 -1.17e-17
55  -4.47e-17  4.47e-17  3.77e-18  4.53e-02  2.52e-17 -2.55e-17 -1.15e-17
56  -9.64e-17  8.21e-17  5.90e-17  1.05e-02  6.42e-17  1.81e-17  1.49e-17
57   2.44e-16 -6.90e-17 -2.11e-16  4.46e-02 -2.33e-16 -1.21e-16 -2.88e-16
58   2.15e-16 -2.00e-16 -3.31e-16 -1.32e-16  2.99e-01  1.88e-18  2.23e-17
59   8.66e-17 -5.66e-17 -9.05e-17 -3.16e-18  3.58e-02 -8.91e-18  7.75e-19
60   9.42e-17 -4.65e-17 -1.12e-16 -1.14e-16  4.16e-02 -8.02e-17 -8.99e-17
61  -7.21e-02  5.10e-02  5.10e-02  5.10e-02  5.10e-02  2.93e-01 -4.93e-16
62   1.72e-02 -1.22e-02 -1.22e-02 -1.22e-02 -1.22e-02 -6.98e-02  9.14e-17
63   1.10e-01 -7.76e-02 -7.76e-02 -7.76e-02 -7.76e-02 -4.46e-01  4.91e-16
64  -2.74e-16 -9.86e-02  3.66e-16  3.15e-16  5.75e-17  3.68e-17  4.78e-17
65  -1.98e-18 -2.46e-04  1.08e-18  1.68e-18  1.33e-18  7.09e-19  7.08e-19
66  -4.54e-17 -1.29e-02  1.83e-17  4.59e-17  2.47e-17  4.92e-17  5.09e-17
67  -7.15e-17 -9.65e-18 -2.39e-02 -5.15e-17 -9.66e-18  1.60e-16  1.86e-16
68   3.01e-17 -6.49e-18  1.24e-02 -2.49e-17 -2.74e-17  1.57e-17 -1.64e-17
69  -6.58e-17  1.79e-17  4.03e-02  1.88e-17  2.18e-17 -9.45e-17 -1.41e-16
70   1.97e-17  2.80e-16 -5.56e-18 -4.45e-02  1.57e-16 -1.58e-16 -6.31e-17
71   6.38e-17 -1.39e-16  2.64e-17 -3.34e-02 -1.13e-16 -1.05e-16 -1.67e-17
72  -4.41e-19 -4.02e-17  1.21e-17 -1.53e-02 -4.96e-18 -3.09e-17  2.05e-17
73  -1.38e-16  1.17e-16  9.38e-17  1.10e-16 -2.49e-02  8.77e-17  3.80e-17
74   2.80e-17 -8.40e-18 -2.30e-17 -2.31e-17  7.07e-03 -1.62e-17 -1.62e-17
75  -9.15e-18  9.60e-19  2.03e-17  1.30e-17 -5.89e-03  1.94e-17  8.20e-18
76  -2.59e-02  1.83e-02  1.83e-02  1.83e-02  1.83e-02  1.05e-01 -2.91e-16
77   6.98e-02 -4.94e-02 -4.94e-02 -4.94e-02 -4.94e-02 -2.84e-01  3.26e-16
78   1.94e-01 -1.37e-01 -1.37e-01 -1.37e-01 -1.37e-01 -7.89e-01  9.34e-16
79   3.00e-17  1.53e-02 -2.15e-17 -3.62e-17 -1.93e-17 -4.59e-18 -2.52e-17
80   2.47e-16  5.30e-02 -1.17e-16 -1.89e-16 -1.48e-16 -1.86e-16 -1.36e-16
81   4.28e-16  1.88e-01 -3.61e-16 -2.33e-16 -2.70e-16 -7.18e-16 -6.99e-16
82  -5.25e-17 -3.01e-17 -3.94e-02 -2.22e-17  4.29e-17  1.10e-16  1.76e-16
83  -5.67e-17  1.97e-17 -1.81e-02  3.75e-17  5.38e-17  2.38e-17  3.93e-17
84  -1.10e-16  5.76e-17 -5.29e-02  6.77e-18  1.03e-16  8.64e-17  1.45e-16
85   3.13e-18 -3.71e-17 -1.41e-17  5.66e-03 -3.99e-18  2.28e-17  1.07e-17
86  -4.15e-17  1.09e-16  2.97e-17  2.55e-02  2.31e-17  5.95e-17  4.63e-18
87  -2.70e-18  3.29e-17  3.16e-18  1.27e-02  6.51e-18  2.59e-17 -6.45e-18
88  -5.32e-16 -1.18e-16  1.52e-16  3.99e-16 -9.15e-03  5.29e-18 -1.12e-16
89  -3.23e-16 -2.86e-16  2.26e-16  3.25e-16  1.71e-02 -1.80e-16 -1.94e-16
90   8.85e-16 -8.89e-17 -3.42e-19 -4.91e-16 -2.41e-02 -3.52e-17  1.69e-16
91  -7.65e-01  5.41e-01  5.41e-01  5.41e-01  5.41e-01 -4.89e-15 -3.88e-01
92  -1.33e-01  9.39e-02  9.39e-02  9.39e-02  9.39e-02 -3.99e-15  5.39e-01
93   2.27e-02 -1.60e-02 -1.60e-02 -1.60e-02 -1.60e-02 -3.36e-17 -9.22e-02
94  -1.56e-16 -9.50e-02  7.34e-17  9.47e-17  6.89e-17  1.60e-16  1.08e-16
95   4.92e-16 -7.55e-02 -2.51e-16 -3.00e-16 -2.47e-16 -3.58e-16 -3.08e-16
96   1.08e-17  9.08e-03 -2.43e-17  1.18e-17  7.58e-18  1.52e-17  6.18e-17
97   1.11e-16 -5.61e-17  3.48e-01 -1.29e-16 -9.92e-17  1.51e-16 -1.35e-16
98  -8.44e-17  7.28e-17 -1.56e-02  5.29e-17  4.87e-17 -7.93e-18  4.06e-17
99  -4.83e-17  3.15e-17 -1.18e-02  4.57e-17  3.49e-17 -2.84e-17 -1.16e-17
100 -3.30e-16  3.20e-16 -2.50e-17  3.00e-01  1.58e-16 -4.64e-17 -4.02e-17
101  2.85e-16 -2.61e-16 -1.85e-16 -4.71e-02 -1.87e-16  1.07e-16  1.20e-16
102 -4.61e-17 -1.57e-18  4.70e-17 -1.38e-02  2.80e-17  8.34e-17  1.12e-16
103  7.53e-16 -6.35e-16 -9.54e-16 -5.61e-16  6.35e-01 -2.30e-16 -2.78e-17
104  1.12e-17 -8.37e-18 -5.09e-18 -2.75e-18  3.46e-03 -4.56e-18  6.57e-19
105 -2.27e-16  1.71e-16  1.40e-16  2.15e-16 -6.59e-02  9.98e-17  1.64e-16
106  5.69e-02 -4.03e-02 -4.03e-02 -4.03e-02 -4.03e-02  4.64e-16 -2.31e-01
107 -2.19e-02  1.55e-02  1.55e-02  1.55e-02  1.55e-02 -9.72e-17  8.88e-02
108 -6.44e-02  4.56e-02  4.56e-02  4.56e-02  4.56e-02 -2.63e-16  2.62e-01
109  2.59e-16  1.19e-01 -5.61e-16 -3.99e-16 -4.45e-17 -1.42e-16  1.79e-17
110  1.36e-16  1.43e-02 -1.02e-16 -1.02e-16 -1.10e-16 -6.86e-17 -4.96e-17
111 -3.56e-16 -7.80e-02  3.33e-16  2.36e-16  2.38e-16  3.34e-16  2.36e-16
112  3.93e-16 -7.28e-17  1.06e-01  1.52e-16  1.89e-17 -4.64e-16 -5.38e-16
113 -3.56e-17  2.01e-17  1.06e-02  1.69e-17  3.92e-17  5.42e-18 -8.01e-19
114 -2.77e-17 -5.42e-18  1.49e-02 -1.35e-18  7.89e-18  3.14e-17  1.02e-17
115  1.41e-17 -3.11e-16  4.20e-17  4.38e-02 -7.13e-17  8.59e-17  8.57e-17
116 -1.16e-17  1.86e-17  5.54e-18  2.77e-03  1.58e-17 -1.43e-18 -2.69e-18
117  2.33e-18  5.59e-18 -1.34e-18  2.67e-03  7.63e-19 -7.36e-19 -4.89e-18
118  2.05e-17 -4.05e-17  3.79e-17 -3.31e-18  1.88e-02 -1.95e-17  1.31e-17
119 -2.08e-16  8.51e-17  1.68e-16  2.11e-16 -5.98e-02  2.32e-16  1.91e-16
120 -2.51e-17  1.87e-17  2.95e-17  1.27e-17 -9.61e-03  2.00e-17  2.05e-17
121  1.02e-01 -7.18e-02 -7.18e-02 -7.18e-02 -7.18e-02  1.20e-15 -4.13e-01
122  5.50e-02 -3.89e-02 -3.89e-02 -3.89e-02 -3.89e-02  1.43e-16 -2.23e-01
123 -1.15e-01  8.11e-02  8.11e-02  8.11e-02  8.11e-02 -4.67e-16  4.66e-01
124  1.29e-16  3.18e-02 -9.97e-17 -1.45e-16 -1.01e-16 -8.18e-17 -6.25e-17
125  1.42e-16  3.42e-02 -1.20e-16 -1.11e-16 -1.11e-16 -1.95e-16 -1.19e-16
126 -4.58e-16 -6.52e-02  4.65e-16  3.44e-16  3.65e-16  3.13e-16  1.48e-16
127 -3.58e-16  2.50e-16 -5.63e-02  2.55e-16  2.66e-16  7.20e-17  1.55e-16
128 -3.08e-18  1.21e-18 -1.50e-02  1.46e-17 -2.57e-18  1.29e-17  2.67e-17
129  2.93e-17 -2.07e-17  1.25e-02 -2.65e-17 -2.16e-17  4.92e-18 -6.64e-18
130 -1.80e-17 -3.23e-16 -5.52e-17  4.57e-02 -2.41e-17  3.96e-17  2.82e-17
131  2.95e-17  1.17e-17 -9.20e-18  1.58e-02 -1.91e-17 -3.12e-17 -4.30e-17
132 -5.14e-18 -3.97e-17 -7.69e-18 -1.23e-02  3.94e-18 -3.82e-18  2.37e-18
133  3.06e-15  7.05e-16 -7.54e-16 -2.15e-15  5.04e-02 -5.13e-17  5.63e-16
134 -5.37e-16 -6.81e-16  3.80e-16  6.53e-16  3.49e-02 -3.76e-16 -4.02e-16
135 -3.71e-15  2.49e-16  1.32e-17  2.19e-15  1.08e-01  4.92e-16 -5.90e-16
     dfb.mnj2  dfb.mnj3  dfb.blq2  dfb.blq3 dfb.ntrgn50.v2 dfb.ntrgn80.v2
1    5.89e-15  5.72e-15  7.45e-01  7.45e-01      -3.04e-01      -3.04e-01
2   -4.44e-15  1.26e-15 -1.58e-15 -1.09e-15      -3.31e-01      -3.31e-01
3   -3.82e-15 -7.09e-15  2.31e-15  2.02e-15      -2.28e-01      -2.28e-01
4    2.13e-15  1.69e-15 -2.25e-17 -5.13e-16       2.14e-01      -4.70e-16
5    2.93e-15  4.53e-15 -7.47e-16  4.69e-16       4.68e-01       4.89e-16
6    3.92e-16  8.74e-16  7.18e-17  1.16e-16       9.04e-02       4.97e-16
7   -4.23e-16 -5.25e-16 -9.77e-17 -1.98e-16      -1.86e-16      -7.16e-02
8   -7.14e-17 -6.32e-17  1.38e-17  1.79e-17       4.62e-19       8.11e-03
9   -1.81e-16 -3.87e-16  5.96e-17  4.15e-17      -1.48e-17       2.08e-02
10   1.10e-16  1.94e-16  1.98e-15  1.33e-15      -2.55e-16      -2.07e-17
11  -5.94e-16 -2.36e-16 -5.46e-16 -6.06e-16      -4.37e-18      -1.75e-17
12  -3.07e-16 -2.53e-16 -3.30e-17 -4.39e-17       3.61e-16       1.25e-16
13   5.55e-16  4.17e-16  4.15e-16  2.91e-16      -4.93e-16      -4.21e-16
14  -2.65e-16 -2.23e-16 -5.94e-17 -7.85e-17       9.43e-17      -3.15e-17
15  -9.25e-17 -4.12e-17 -2.87e-17  5.55e-19      -6.21e-17      -2.37e-18
16   1.32e-16  1.14e-16 -1.05e-01 -1.88e-16      -4.30e-02      -4.30e-02
17  -4.42e-19  8.71e-18 -1.24e-16 -1.20e-16      -1.34e-02      -1.34e-02
18  -1.43e-16 -5.15e-17  1.01e-15  9.06e-16       1.27e-01       1.27e-01
19   2.46e-16  4.39e-16 -3.46e-17  3.91e-17      -7.48e-02       1.23e-16
20   1.46e-16  1.72e-16 -1.06e-16 -1.28e-16      -5.69e-02       4.38e-17
21  -1.60e-15 -1.81e-15 -2.66e-16 -9.40e-17       3.72e-01      -3.46e-16
22  -9.76e-16 -1.11e-15  9.28e-16  7.44e-16      -2.53e-16      -3.28e-01
23  -2.55e-16 -2.72e-16  6.00e-17  7.27e-17       1.06e-17      -9.34e-02
24  -2.29e-16 -5.87e-16  1.61e-16  2.03e-16       1.93e-17      -2.25e-01
25   5.57e-18  1.88e-18  1.01e-18  2.87e-18       2.08e-18      -9.59e-19
26  -3.41e-17  7.97e-17 -1.74e-16 -3.20e-16      -3.68e-17       5.13e-17
27   1.12e-16  7.48e-17 -6.74e-17 -4.45e-17      -2.26e-17       1.51e-17
28  -9.05e-17 -1.15e-16  1.41e-18  2.05e-17      -1.36e-19      -1.56e-18
29  -6.05e-16 -3.38e-16 -1.23e-17  2.38e-17      -1.37e-16       1.63e-17
30   2.02e-16  1.33e-16  2.87e-17  4.39e-18      -3.30e-17       1.22e-17
31  -6.76e-16 -2.58e-16  8.03e-16  5.28e-01       2.16e-01       2.16e-01
32  -3.59e-16 -6.18e-16  2.65e-15  2.65e-15       3.63e-01       3.63e-01
33  -5.64e-16 -4.98e-16  1.49e-15  1.60e-15       2.13e-01       2.13e-01
34   7.19e-16  8.32e-16  1.23e-16  2.39e-16      -1.92e-01       2.46e-16
35   1.11e-15  1.46e-15  1.80e-16  3.26e-16      -3.59e-01       3.42e-16
36   1.56e-15  2.08e-15  1.50e-16  3.45e-16      -4.59e-01       4.92e-16
37   3.94e-16  4.01e-16 -1.99e-16 -2.83e-16       1.46e-16       3.95e-01
38  -5.50e-17  5.07e-16  1.46e-16 -2.71e-17       2.69e-17       1.35e-01
39   6.48e-16  7.95e-16  1.05e-16  4.84e-17       2.33e-17       1.63e-01
40  -2.93e-17  6.09e-16  3.77e-16  1.13e-16      -6.25e-17       1.23e-17
41   5.13e-16 -6.78e-17  7.92e-17  2.42e-17       7.89e-17      -9.89e-18
42   4.55e-19  1.72e-18  1.63e-18 -1.08e-19       5.48e-19      -3.25e-19
43  -4.09e-01 -4.09e-01  9.42e-16  8.46e-16       1.44e-15      -4.61e-17
44   5.19e-01  4.87e-16 -2.47e-16 -3.26e-16      -5.67e-16      -2.67e-16
45  -1.50e-15  8.23e-01 -9.84e-16 -1.12e-15      -1.68e-15       3.49e-16
46   5.92e-15  5.56e-15 -1.47e+00 -1.47e+00      -5.99e-01      -5.99e-01
47   2.82e-16 -7.14e-17  1.20e-16  7.31e-17       4.79e-02       4.79e-02
48  -2.90e-15 -4.98e-15  1.66e-15  1.34e-15      -2.95e-01      -2.95e-01
49   1.15e-15  1.10e-15 -2.49e-17 -2.74e-16       2.63e-01       2.28e-16
50   3.95e-16  6.75e-16  3.47e-17  2.49e-16       1.52e-01       2.09e-16
51   2.52e-16  6.30e-16  1.01e-16  1.39e-16       1.28e-01       2.84e-16
52  -8.85e-16 -1.24e-15  4.16e-16  1.53e-16       1.42e-16      -2.50e-01
53   1.93e-16  1.96e-16 -5.86e-17 -9.76e-17      -2.36e-17      -5.51e-02
54   1.50e-16  2.96e-16 -6.50e-17 -4.85e-17      -1.32e-17      -2.72e-02
55   2.99e-17  1.38e-17  9.70e-17  7.37e-17       3.18e-17       6.77e-18
56   6.72e-17  3.33e-17  9.84e-17  1.55e-16      -1.72e-17      -2.51e-17
57  -2.40e-16 -2.00e-16 -1.18e-16 -1.53e-16       9.09e-17       7.46e-17
58   3.82e-17  1.04e-16 -1.17e-16  6.47e-18       3.11e-18       5.16e-17
59  -1.67e-16 -1.04e-16 -2.55e-17 -4.15e-17      -4.65e-17       5.53e-18
60  -3.00e-17 -1.62e-16  6.43e-17  4.98e-17      -2.06e-18       3.16e-17
61   3.53e-16  4.64e-16  5.07e-01 -1.36e-15      -2.07e-01      -2.07e-01
62  -4.71e-17 -3.79e-17  2.31e-16  1.93e-16       4.94e-02       4.94e-02
63  -2.11e-16 -1.53e-17  9.83e-16  1.18e-15       3.15e-01       3.15e-01
64  -9.46e-16 -1.19e-15  6.01e-16  3.24e-16       4.01e-01       1.02e-16
65  -1.69e-18 -1.76e-18  8.88e-19  1.78e-18       1.00e-03      -5.77e-19
66  -5.83e-17 -1.10e-16 -6.06e-18  1.83e-17       5.25e-02      -3.06e-17
67   8.46e-17  1.77e-16 -1.06e-16 -7.41e-17      -7.21e-17       9.72e-02
68  -4.91e-17 -4.26e-17 -3.34e-17 -2.15e-17      -3.30e-17      -5.03e-02
69  -6.24e-17  4.63e-17  1.99e-16  1.51e-16       2.80e-17      -1.64e-01
70   1.45e-16  1.91e-17  7.86e-17  8.01e-17      -1.04e-16       1.60e-16
71   4.98e-17  9.85e-17 -4.40e-17 -1.64e-16       9.93e-17       7.19e-17
72   5.49e-17  3.99e-18 -1.91e-17  2.74e-17       3.48e-17       2.56e-17
73  -1.76e-16 -2.22e-16  2.04e-16  1.46e-16      -9.48e-17      -4.92e-17
74   3.15e-17  8.24e-18 -1.82e-17 -7.70e-18       3.13e-18       7.67e-18
75   3.39e-17  1.98e-17 -4.98e-18 -2.96e-18      -8.07e-18      -1.16e-17
76   1.49e-16  1.69e-16 -4.98e-16  1.82e-01      -7.44e-02      -7.44e-02
77  -3.83e-17 -1.35e-16  7.78e-16  8.36e-16       2.01e-01       2.01e-01
78  -5.71e-16 -3.20e-16  2.05e-15  2.58e-15       5.58e-01       5.58e-01
79   8.55e-17  1.12e-16 -2.18e-17  1.93e-17      -6.22e-02      -1.80e-18
80  -1.11e-17  3.66e-16 -1.68e-16 -7.63e-17      -2.15e-01       1.01e-16
81   1.82e-15  2.24e-15  5.58e-17  3.88e-16      -7.62e-01       3.11e-16
82   3.64e-16  2.43e-16 -3.58e-17 -1.36e-16      -4.10e-17       1.60e-01
83  -5.69e-17  1.33e-16  1.52e-17 -5.64e-19       1.05e-17       7.34e-02
84   4.12e-16  7.10e-16  6.30e-17  2.76e-17       2.45e-17       2.15e-01
85   3.72e-17  5.56e-17 -8.38e-18 -3.92e-17      -7.63e-19      -1.35e-17
86   2.18e-16  8.54e-18  6.01e-17  3.73e-17      -5.93e-17      -4.87e-17
87  -3.05e-17 -3.77e-18  2.93e-17 -1.29e-17      -2.88e-17      -2.72e-17
88  -9.11e-02 -9.11e-02  2.06e-16  1.88e-16       3.00e-16      -9.75e-18
89  -1.70e-01  3.20e-17  1.93e-16  1.89e-16       2.42e-16       1.02e-16
90  -2.04e-16  2.39e-01 -3.67e-16 -3.07e-16      -5.98e-16       3.98e-17
91  -2.39e-15 -2.12e-15  6.72e-01  6.72e-01       3.85e-15       3.11e-15
92  -2.62e-15  9.67e-16 -7.49e-16 -4.79e-16       3.56e-15       3.20e-15
93   4.44e-16  9.05e-16 -3.83e-16 -3.54e-16      -2.60e-17       2.71e-17
94  -3.13e-16 -2.21e-16  3.05e-17  9.68e-17       2.28e-17      -3.48e-17
95   9.37e-16  1.40e-15 -9.91e-17  3.18e-16       1.55e-16       2.66e-16
96  -5.77e-17 -1.63e-16 -2.50e-17 -1.96e-17      -1.25e-16      -6.23e-17
97   3.95e-16  5.40e-16 -1.52e-16 -1.48e-17      -7.46e-17      -1.82e-16
98  -2.63e-16 -2.59e-16  5.42e-17  5.08e-17       1.08e-17      -2.52e-17
99  -1.86e-16 -3.96e-16  5.86e-17  4.39e-17       2.78e-17      -7.59e-18
100  4.57e-17  1.11e-16  6.70e-16  4.98e-16       1.35e-16      -2.07e-17
101 -4.25e-16 -1.38e-16 -3.83e-16 -5.93e-16      -3.42e-17       8.69e-18
102  3.52e-17  1.40e-17 -1.92e-17  2.39e-19      -5.52e-17      -4.98e-17
103 -9.03e-17  5.65e-17 -5.04e-16 -3.47e-16       1.92e-16       3.41e-16
104 -6.54e-18 -1.11e-17 -4.83e-18 -7.83e-18       2.06e-19       9.64e-19
105 -2.35e-16 -3.28e-16  7.40e-17  6.61e-18      -4.98e-18       1.15e-17
106 -2.79e-16 -3.07e-16 -4.01e-01  9.72e-16      -3.90e-16      -4.21e-16
107 -1.60e-17 -2.24e-17 -2.87e-16 -2.60e-16       1.33e-16       1.17e-16
108  9.30e-17  8.69e-17 -6.69e-16 -6.67e-16       3.53e-16       2.96e-16
109  8.91e-16  1.26e-15 -5.14e-16 -2.39e-16       4.91e-16      -1.61e-17
110  6.35e-17  8.75e-17 -8.70e-17 -9.56e-17       6.46e-17       6.39e-17
111 -7.79e-16 -9.99e-16  7.13e-17  3.44e-17      -4.56e-16      -2.48e-16
112 -5.97e-16 -9.99e-16  2.12e-16  1.20e-16       3.08e-16       5.63e-16
113 -4.65e-17 -5.52e-17  4.91e-17  3.95e-17      -4.66e-18       1.46e-17
114 -9.82e-17 -1.16e-16  3.71e-18  1.93e-17      -2.20e-17      -7.63e-18
115 -3.09e-16 -2.05e-16 -1.35e-16 -8.92e-17       1.32e-16      -1.39e-16
116  7.42e-18  8.83e-19  1.19e-17  2.22e-17      -2.45e-18      -5.51e-19
117 -8.54e-18 -1.12e-17 -6.12e-19 -2.11e-19      -3.19e-18      -1.42e-18
118  1.33e-16  2.17e-16 -5.76e-17 -4.59e-17       4.70e-17      -1.34e-17
119 -4.49e-16 -2.42e-16 -6.40e-18  4.98e-17      -1.05e-16      -1.37e-16
120  7.66e-17  5.32e-17  6.70e-18  8.58e-18      -6.17e-18      -5.01e-18
121 -5.20e-16 -2.75e-16  2.09e-15 -7.15e-01      -6.41e-16      -6.06e-16
122 -3.46e-17  9.91e-18  5.83e-16  6.03e-16      -2.66e-16      -1.97e-16
123  6.48e-16  5.09e-16 -9.36e-16 -8.72e-16       6.53e-16       5.67e-16
124  2.28e-16  1.84e-16 -6.42e-17 -2.40e-17       1.46e-16       4.94e-17
125  3.07e-16  3.26e-16  7.90e-18 -1.84e-17       2.18e-16       1.41e-16
126 -5.36e-16 -5.85e-16  2.14e-16  3.02e-16      -3.68e-16      -1.86e-16
127  3.37e-16  6.32e-17  3.42e-16  1.68e-16      -1.01e-16      -9.11e-17
128 -7.59e-17  9.51e-17 -3.46e-18 -2.46e-17      -6.59e-18      -3.89e-17
129 -7.03e-17 -7.11e-17 -2.64e-17 -3.93e-17      -1.96e-18       1.01e-17
130  2.63e-16  2.48e-16  4.08e-17 -1.34e-16       9.05e-17      -5.60e-17
131 -3.44e-17 -5.93e-18  2.17e-17 -8.38e-18       3.96e-18       5.20e-18
132  3.79e-18 -7.65e-17 -2.56e-17  8.18e-18       2.06e-17       1.35e-17
133  5.02e-01  5.02e-01 -1.04e-15 -9.68e-16      -1.62e-15       5.44e-17
134 -3.47e-01 -5.45e-17  3.43e-16  3.38e-16       5.08e-16       1.92e-16
135  5.89e-16 -1.08e+00  1.42e-15  1.15e-15       2.52e-15      -4.83e-16
    dfb.ntrgn110.v2 dfb.ntrgn140.v2 dfb.ntrgn50.v3 dfb.ntrgn80.v3
1         -3.04e-01       -3.04e-01      -3.04e-01      -3.04e-01
2         -3.31e-01       -3.31e-01      -3.31e-01      -3.31e-01
3         -2.28e-01       -2.28e-01      -2.28e-01      -2.28e-01
4          4.50e-17       -4.72e-16       2.14e-01      -1.76e-16
5          5.10e-16        5.32e-17       4.68e-01       2.65e-16
6          5.78e-16        5.22e-16       9.04e-02       1.96e-16
7         -1.33e-16       -1.50e-16      -3.82e-16      -7.16e-02
8          7.13e-19        9.91e-19      -8.54e-18       8.11e-03
9         -2.75e-17       -2.33e-17      -2.33e-17       2.08e-02
10         1.76e-01       -1.51e-16      -1.85e-16      -4.77e-17
11         1.48e-01        5.60e-17      -7.86e-17      -6.05e-17
12        -1.25e-01        2.38e-16       4.28e-16       1.52e-16
13        -6.65e-16        4.84e-01      -2.26e-16      -2.19e-16
14        -9.97e-18       -1.60e-01       2.92e-17      -4.67e-17
15        -2.43e-17        9.72e-02      -8.59e-17      -1.87e-17
16        -4.30e-02       -4.30e-02      -4.30e-02      -4.30e-02
17        -1.34e-02       -1.34e-02      -1.34e-02      -1.34e-02
18         1.27e-01        1.27e-01       1.27e-01       1.27e-01
19         1.31e-16        8.83e-17      -7.48e-02       7.51e-17
20         5.47e-17        4.72e-17      -5.69e-02       3.13e-17
21        -4.39e-16       -3.10e-16       3.72e-01      -2.64e-16
22        -1.77e-16       -1.71e-16      -1.08e-16      -3.28e-01
23         2.29e-17        3.68e-17       5.53e-17      -9.34e-02
24         4.28e-17        1.18e-16       7.42e-17      -2.25e-01
25         2.71e-03        2.29e-19       9.68e-19      -1.85e-18
26         1.24e-01        4.73e-17      -4.90e-17       1.69e-17
27         5.13e-02        7.13e-18      -2.70e-17       6.98e-18
28        -4.69e-18        2.51e-02      -1.38e-19      -4.71e-18
29        -2.67e-17        2.14e-01      -1.28e-16      -4.44e-17
30        -7.87e-18        6.30e-02      -2.95e-17       2.77e-18
31         2.16e-01        2.16e-01       2.16e-01       2.16e-01
32         3.63e-01        3.63e-01       3.63e-01       3.63e-01
33         2.13e-01        2.13e-01       2.13e-01       2.13e-01
34         2.57e-16        2.50e-16      -1.92e-01       1.63e-16
35         4.43e-16        3.50e-16      -3.59e-01       2.43e-16
36         5.66e-16        4.38e-16      -4.59e-01       2.87e-16
37         8.56e-17        3.81e-17       1.30e-17       3.95e-01
38         3.07e-18       -2.22e-17      -4.88e-17       1.35e-01
39        -1.20e-17       -4.14e-17      -1.61e-17       1.63e-01
40        -2.09e-01        5.50e-18      -6.43e-18       5.69e-17
41        -1.68e-01       -1.94e-17       8.58e-17       1.14e-17
42        -1.38e-03       -4.60e-19       5.20e-19      -2.81e-19
43         3.34e-16       -1.67e-01       1.56e-15       3.50e-17
44        -2.38e-16       -2.12e-01      -6.93e-16      -3.18e-16
45        -3.78e-16       -3.36e-01      -1.71e-15       4.95e-16
46        -5.99e-01       -5.99e-01      -7.30e-15      -6.63e-15
47         4.79e-02        4.79e-02      -3.61e-16      -3.27e-16
48        -2.95e-01       -2.95e-01       5.62e-16       3.09e-16
49         4.20e-16        2.11e-16       1.53e-16       4.79e-16
50         1.57e-16        2.53e-16       4.52e-17       1.58e-16
51         3.96e-16        3.29e-16       2.92e-16       1.04e-16
52         2.05e-16        2.34e-16      -9.18e-17      -1.02e-16
53        -3.33e-18       -1.29e-17       1.25e-17       2.69e-17
54        -2.49e-18       -2.79e-18       4.73e-19       2.83e-17
55         2.30e-02        2.43e-17       1.56e-17       1.01e-18
56        -4.27e-02        7.40e-18      -3.96e-17      -2.29e-17
57        -1.81e-01        2.27e-16       2.59e-16       1.61e-16
58         4.75e-17        1.52e-01      -2.78e-17       1.01e-17
59        -9.08e-18       -1.45e-01      -5.32e-17      -5.52e-18
60         9.49e-17       -1.69e-01      -3.47e-18       5.09e-17
61        -2.07e-01       -2.07e-01       3.62e-16       2.40e-16
62         4.94e-02        4.94e-02      -1.22e-16      -9.51e-17
63         3.15e-01        3.15e-01      -7.15e-16      -3.22e-16
64         3.23e-17       -1.17e-16      -3.36e-16       1.20e-16
65        -6.58e-19       -6.23e-19      -5.26e-19      -2.43e-19
66        -3.26e-17       -4.14e-17      -5.63e-17      -2.15e-17
67        -9.31e-17       -9.82e-17      -1.10e-16      -1.68e-16
68        -1.73e-17       -1.52e-17      -1.67e-20       3.49e-18
69         6.12e-17        1.32e-17       7.81e-17       1.45e-16
70         1.81e-01        2.32e-17      -1.26e-16       1.10e-16
71         1.36e-01        2.67e-17       6.68e-17       3.98e-17
72         6.22e-02       -5.30e-18       8.57e-18      -9.81e-18
73        -7.59e-17        1.01e-01      -6.35e-17      -4.42e-17
74         1.79e-17       -2.87e-02       2.82e-18       5.68e-18
75        -1.79e-17        2.39e-02      -4.02e-19      -4.74e-18
76        -7.44e-02       -7.44e-02       1.30e-16       8.27e-17
77         2.01e-01        2.01e-01      -4.52e-16      -2.42e-16
78         5.58e-01        5.58e-01      -1.31e-15      -6.33e-16
79         8.04e-18        1.35e-18       1.09e-17      -5.28e-18
80         1.25e-16        1.33e-16       1.45e-16       2.28e-17
81         4.06e-16        4.90e-16       8.09e-16       2.57e-16
82        -8.65e-17       -8.05e-17      -1.10e-16      -1.39e-16
83         1.57e-19        4.16e-19      -2.05e-17      -2.26e-17
84        -5.97e-18        1.05e-17      -6.25e-17      -1.38e-16
85        -2.30e-02       -6.78e-18       3.49e-18      -7.11e-18
86        -1.03e-01       -1.32e-17      -3.94e-17      -2.49e-17
87        -5.14e-02        1.26e-18      -1.46e-17      -3.57e-18
88         6.27e-17        3.72e-02       3.26e-16      -5.38e-18
89         1.35e-16       -6.96e-02       2.62e-16       1.24e-16
90        -2.26e-16        9.78e-02      -5.64e-16       1.04e-16
91         3.39e-15        3.46e-15       2.74e-01       2.74e-01
92         3.35e-15        3.36e-15      -3.81e-01      -3.81e-01
93         6.87e-17        2.30e-17       6.52e-02       6.52e-02
94        -7.26e-17       -3.24e-17      -4.82e-02      -8.71e-17
95         2.28e-16        4.05e-16       3.07e-01       1.96e-16
96        -9.71e-17       -7.88e-17      -3.69e-02      -1.47e-17
97        -9.85e-17       -1.03e-16       1.28e-16       1.77e-01
98         3.65e-18        2.14e-17      -2.70e-17       6.32e-02
99         2.07e-17        2.45e-17       9.49e-18       4.80e-02
100        4.45e-17        1.27e-16       1.01e-16       4.14e-17
101       -2.93e-17       -8.25e-17       4.11e-17       1.30e-17
102       -6.93e-17       -6.88e-17      -8.97e-17      -5.70e-17
103        3.42e-16        4.65e-17       1.12e-17       2.06e-16
104       -8.77e-19        9.11e-18      -4.90e-18      -4.95e-18
105       -1.20e-16       -5.79e-17      -3.37e-18      -3.86e-17
106       -2.63e-16       -4.26e-16       1.64e-01       1.64e-01
107        7.79e-17        1.09e-16      -6.28e-02      -6.28e-02
108        2.58e-16        3.08e-16      -1.85e-01      -1.85e-01
109       -2.43e-20        2.24e-16      -4.81e-01      -5.08e-17
110        5.74e-17        5.80e-17      -5.79e-02       4.41e-17
111       -2.09e-16       -2.83e-16       3.17e-01      -1.91e-16
112        2.75e-16        2.70e-16       3.69e-16      -4.31e-01
113       -2.10e-19       -9.24e-18       2.83e-18      -4.30e-02
114       -1.88e-17       -3.62e-17      -3.99e-18      -6.06e-02
115       -1.31e-16       -6.19e-17       6.59e-17      -1.81e-16
116       -1.62e-18       -4.16e-19      -3.73e-18      -3.06e-18
117       -1.18e-18       -1.00e-18      -1.97e-18      -7.38e-19
118        2.43e-17       -5.49e-18       1.88e-17      -3.32e-17
119       -2.23e-16       -2.45e-16      -3.90e-17      -7.97e-17
120       -1.73e-17       -2.53e-17      -2.12e-18      -4.69e-18
121       -9.60e-16       -8.65e-16       2.92e-01       2.92e-01
122       -1.59e-16       -2.40e-16       1.58e-01       1.58e-01
123        4.24e-16        6.44e-16      -3.29e-01      -3.29e-01
124        6.43e-17        5.88e-17      -1.29e-01       2.86e-17
125        1.39e-16        1.46e-16      -1.39e-01       8.91e-17
126       -2.07e-16       -2.35e-16       2.65e-01      -1.05e-16
127       -1.09e-16       -8.35e-17      -1.58e-16       2.29e-01
128       -1.51e-17       -4.64e-18      -2.21e-17       6.10e-02
129       -3.08e-18       -1.17e-17       1.01e-17      -5.09e-02
130       -3.84e-17       -5.37e-17       7.29e-17      -5.05e-17
131        1.35e-17        1.91e-17       0.00e+00       0.00e+00
132        2.90e-17        8.07e-18       2.73e-17       1.70e-17
133       -3.13e-16       -5.91e-16      -1.75e-15       2.84e-17
134        2.46e-16        3.27e-16       5.44e-16       2.16e-16
135        7.24e-16        1.05e-15       2.40e-15      -7.77e-16
    dfb.ntrgn110.v3 dfb.ntrgn140.v3 dfb.ntrgn50.b2 dfb.ntrgn80.b2
1         -3.04e-01       -3.04e-01      -5.27e-01      -5.27e-01
2         -3.31e-01       -3.31e-01       9.89e-16       2.10e-15
3         -2.28e-01       -2.28e-01      -1.67e-15      -1.74e-15
4          1.98e-16       -2.24e-16       3.70e-01      -4.32e-18
5          3.28e-16       -3.08e-17       3.11e-15       3.78e-16
6          2.30e-16        1.90e-16      -4.19e-16      -4.33e-17
7         -2.54e-16       -2.31e-16       4.72e-18      -1.24e-01
8         -5.21e-18       -3.15e-18      -1.65e-17      -4.45e-18
9         -3.69e-17       -2.60e-17      -4.72e-17      -4.21e-17
10         1.76e-01       -1.95e-16      -1.81e-15      -1.31e-15
11         1.48e-01        1.87e-17       2.44e-16       4.20e-16
12        -1.25e-01        2.25e-16       1.10e-16       4.01e-17
13        -5.59e-16        4.84e-01      -9.05e-16      -1.40e-16
14        -1.73e-16       -1.60e-01       6.19e-17       8.09e-17
15        -5.61e-17        9.72e-02       4.12e-17       3.53e-17
16        -4.30e-02       -4.30e-02       7.45e-02       7.45e-02
17        -1.34e-02       -1.34e-02       8.80e-17       8.69e-17
18         1.27e-01        1.27e-01      -6.89e-16      -8.24e-16
19         7.95e-17        4.34e-17       1.30e-01       6.98e-17
20         3.76e-17        3.85e-17       1.09e-16       6.51e-17
21        -3.52e-16       -2.98e-16       5.23e-16       2.88e-17
22        -2.35e-16       -1.71e-16      -8.00e-16       5.69e-01
23         3.49e-17        5.18e-17      -8.02e-17      -1.49e-17
24         2.21e-17        1.28e-16      -2.70e-17      -2.75e-16
25         2.71e-03       -1.88e-19       1.95e-18      -1.48e-18
26         1.24e-01        3.19e-17      -4.63e-18       1.62e-16
27         5.13e-02       -3.20e-18       3.02e-18       5.56e-17
28        -9.03e-18        2.51e-02       1.15e-17      -1.26e-17
29        -4.62e-17        2.14e-01      -8.57e-17       4.22e-17
30        -4.54e-18        6.30e-02      -3.01e-17      -5.95e-17
31         2.16e-01        2.16e-01      -6.50e-16      -6.85e-16
32         3.63e-01        3.63e-01      -1.92e-15      -1.97e-15
33         2.13e-01        2.13e-01      -1.01e-15      -1.09e-15
34         1.64e-16        2.30e-16      -1.26e-16       6.43e-19
35         3.46e-16        2.94e-16      -4.09e-16      -9.33e-17
36         3.83e-16        3.42e-16      -3.07e-16      -2.75e-16
37         7.45e-17       -2.74e-18       4.38e-17      -1.54e-16
38        -1.42e-17       -5.51e-17      -9.58e-17      -1.47e-16
39        -2.04e-17       -4.87e-17      -8.27e-17      -1.32e-16
40        -2.09e-01        5.08e-17      -5.01e-16      -1.76e-16
41        -1.68e-01        2.33e-18       2.18e-18      -9.16e-17
42        -1.38e-03       -3.83e-19      -6.36e-21      -1.16e-18
43         4.46e-16       -1.67e-01      -5.51e-17      -7.97e-16
44        -3.06e-16       -2.12e-01      -2.77e-16       2.37e-16
45        -3.63e-16       -3.36e-01       1.61e-16       5.77e-16
46        -6.82e-15       -7.19e-15       1.04e+00       1.04e+00
47        -3.43e-16       -3.57e-16      -1.03e-16      -1.46e-16
48        -3.73e-17        1.13e-16      -1.27e-15      -1.22e-15
49         6.83e-16        6.59e-16      -4.55e-01       2.75e-17
50         1.10e-16        1.74e-16       4.60e-16      -4.90e-17
51         1.59e-16        1.36e-16      -2.79e-16      -9.11e-17
52         5.55e-17        4.11e-30      -5.10e-16       4.32e-01
53         4.98e-18        1.76e-17       6.41e-17       2.35e-17
54        -5.00e-19        9.63e-18       4.84e-17       4.24e-17
55         5.20e-18        1.98e-17      -7.01e-17      -6.25e-17
56        -2.11e-17       -2.63e-18      -7.41e-17      -6.44e-17
57         2.15e-16        2.73e-16      -1.91e-18       9.85e-17
58        -1.12e-17       -4.43e-17       2.54e-16       1.38e-16
59        -4.27e-17        2.02e-18       2.73e-17       3.27e-17
60         8.25e-17        7.97e-17      -4.66e-17       1.19e-18
61         1.93e-16        5.15e-16      -3.59e-01      -3.59e-01
62        -4.82e-17       -7.26e-17      -1.54e-16      -1.64e-16
63        -3.28e-16       -4.59e-16      -6.38e-16      -7.83e-16
64        -1.43e-17       -1.60e-16       6.94e-01      -5.30e-16
65        -4.82e-19       -3.44e-19      -1.06e-18      -3.21e-19
66        -2.72e-17       -3.00e-17       3.70e-17       1.88e-17
67        -1.10e-16       -1.32e-16       7.68e-17       1.68e-01
68        -1.62e-18        1.19e-17       1.84e-17       4.29e-18
69         7.67e-17        5.69e-17      -8.80e-17      -9.73e-17
70         1.23e-16       -5.14e-17      -2.44e-16      -2.46e-17
71         7.09e-18       -3.77e-18       8.80e-17       1.74e-17
72        -2.44e-17       -2.33e-17       4.06e-17       2.74e-17
73        -2.57e-17       -2.46e-17      -1.94e-16      -1.05e-16
74         1.56e-17        1.91e-17       6.05e-18       1.40e-17
75        -8.52e-18       -5.82e-18       9.43e-18      -4.54e-18
76         1.50e-16        1.44e-16       3.56e-16       2.94e-16
77        -2.07e-16       -3.01e-16      -5.83e-16      -5.14e-16
78        -5.94e-16       -8.87e-16      -1.53e-15      -1.39e-15
79         1.22e-17       -1.06e-17      -3.42e-17      -7.33e-18
80         7.35e-17        6.80e-17       2.01e-16       1.02e-16
81         3.93e-16        3.99e-16      -4.34e-16       1.72e-17
82        -1.02e-16       -1.25e-16       8.95e-17       2.78e-17
83        -1.11e-17       -2.34e-17       7.45e-18       7.82e-18
84        -2.05e-17       -6.56e-17      -1.66e-16       2.81e-17
85        -5.95e-18       -4.15e-18       4.10e-17       1.95e-17
86        -2.32e-17        1.58e-17      -9.35e-17      -7.99e-17
87        -5.53e-18        1.43e-17      -4.20e-17      -3.40e-17
88         8.48e-17        9.63e-17      -5.52e-18      -1.89e-16
89         1.39e-16        1.19e-16       1.07e-17      -1.85e-16
90        -1.62e-16       -2.06e-16       9.31e-17       2.72e-16
91         2.74e-01        2.74e-01      -4.75e-01      -4.75e-01
92        -3.81e-01       -3.81e-01       7.42e-16       1.24e-15
93         6.52e-02        6.52e-02       2.53e-16       2.28e-16
94        -1.28e-16       -1.20e-16       8.35e-02      -1.20e-19
95         2.04e-16        2.69e-16       1.09e-15      -2.11e-17
96        -3.68e-17       -2.74e-17       7.11e-17       3.27e-17
97         2.21e-17        8.46e-17       2.33e-16      -3.06e-01
98        -1.33e-17       -1.36e-17      -6.99e-17      -9.11e-17
99         1.05e-17       -2.00e-18      -4.23e-17      -6.59e-17
100        1.52e-01        1.57e-16      -4.80e-16      -4.35e-16
101        1.92e-01       -6.00e-17       2.78e-16       2.37e-16
102        5.59e-02       -6.79e-17       4.10e-17       5.48e-18
103        9.30e-17        3.23e-01       6.23e-16       4.05e-16
104       -9.11e-18       -1.40e-02       4.50e-18       1.35e-18
105       -1.16e-16        2.68e-01      -1.02e-16      -7.81e-17
106        1.64e-01        1.64e-01       2.83e-01       2.83e-01
107       -6.28e-02       -6.28e-02       2.29e-16       2.49e-16
108       -1.85e-01       -1.85e-01       5.62e-16       5.93e-16
109        1.37e-18        2.47e-16      -8.34e-01       5.94e-16
110        4.31e-17        4.40e-17       8.15e-17       6.24e-17
111       -1.36e-16       -2.11e-16       5.09e-17      -1.44e-16
112        3.92e-16        4.22e-16      -8.52e-17      -7.47e-01
113       -2.14e-20       -4.18e-18      -3.51e-17      -2.85e-17
114       -9.02e-18       -2.31e-17       2.00e-17      -7.88e-18
115       -1.78e-01       -4.94e-17       3.14e-16       8.47e-17
116       -1.13e-02       -1.33e-18      -1.45e-17      -6.54e-18
117       -1.09e-02        4.52e-19      -3.44e-18      -3.19e-18
118       -2.20e-17       -7.62e-02       7.70e-17      -7.59e-18
119       -1.40e-16        2.43e-01       1.86e-17      -1.65e-17
120       -1.41e-17        3.91e-02      -8.45e-18      -1.34e-17
121        2.92e-01        2.92e-01      -1.54e-15      -1.43e-15
122        1.58e-01        1.58e-01      -5.06e-16      -4.76e-16
123       -3.29e-01       -3.29e-01       7.97e-16       8.31e-16
124        5.58e-17        2.51e-17      -1.13e-16      -1.23e-17
125        9.39e-17        1.02e-16      -4.88e-17       9.75e-18
126       -1.05e-16       -1.33e-16      -6.83e-17      -2.60e-16
127       -1.35e-16       -1.32e-16      -1.91e-16      -4.42e-16
128       -2.45e-17       -1.82e-17       4.73e-18      -6.26e-19
129       -1.71e-18       -3.53e-19       3.71e-17       2.96e-17
130       -1.86e-01       -8.76e-17       2.82e-16       6.89e-17
131       -6.41e-02        2.18e-17      -3.11e-17      -4.08e-17
132        5.00e-02        9.02e-18       4.92e-17       3.31e-17
133       -4.58e-16       -2.05e-01      -8.77e-17       9.06e-16
134        2.45e-16       -1.42e-01       7.82e-17      -2.97e-16
135        5.39e-16       -4.40e-01      -1.29e-16      -1.04e-15
    dfb.ntrgn110.b2 dfb.ntrgn140.b2 dfb.ntrgn50.b3 dfb.ntrgn80.b3
1         -5.27e-01       -5.27e-01      -5.27e-01      -5.27e-01
2          2.19e-15        2.15e-15       2.65e-17       1.63e-15
3         -2.40e-15       -2.34e-15      -1.37e-15      -1.06e-15
4          9.41e-16        5.87e-16       3.70e-01       3.08e-16
5          3.44e-16       -1.63e-17       1.13e-15      -4.61e-16
6         -9.34e-17       -9.24e-17      -4.48e-16      -6.43e-17
7          8.74e-17        1.11e-16       8.71e-17      -1.24e-01
8         -1.27e-17       -1.10e-17      -1.57e-17      -1.04e-17
9         -4.50e-17       -4.25e-17      -3.07e-17      -2.75e-17
10         3.04e-01       -1.37e-15      -1.40e-15      -1.01e-15
11         7.40e-16        4.61e-16       3.02e-16       5.57e-16
12         1.65e-16        1.74e-17       1.10e-16       8.33e-17
13        -4.19e-16        8.39e-01      -7.57e-16       1.05e-16
14         1.92e-17        1.30e-16       5.66e-17       1.20e-16
15         3.15e-17        9.43e-17       1.95e-17      -1.19e-17
16         7.45e-02        7.45e-02       1.93e-16       1.25e-16
17         1.00e-16        8.85e-17       8.77e-17       8.31e-17
18        -7.44e-16       -7.29e-16      -6.35e-16      -7.05e-16
19         9.58e-17        3.65e-17       7.90e-18      -7.63e-18
20         7.19e-17        8.95e-17       1.27e-16       1.12e-16
21        -2.82e-16        3.65e-16       4.66e-16       1.34e-16
22        -1.12e-15       -8.60e-16      -4.56e-16      -4.89e-16
23        -4.53e-18       -1.11e-16      -2.74e-17      -5.41e-17
24        -1.93e-16       -7.71e-17       1.15e-17      -2.61e-16
25        -4.70e-03       -8.29e-19       1.00e-18      -4.04e-18
26         1.59e-16        1.49e-16       8.09e-17       2.96e-16
27         9.57e-17        6.31e-17      -2.43e-17       3.11e-17
28        -7.23e-18       -4.34e-02      -1.14e-17      -2.04e-17
29         5.31e-17       -3.09e-16      -5.82e-17       1.32e-17
30        -2.68e-17       -4.18e-17      -4.68e-18      -4.43e-17
31        -4.48e-16       -7.85e-16      -3.73e-01      -3.73e-01
32        -1.84e-15       -2.05e-15      -2.04e-15      -1.93e-15
33        -1.13e-15       -1.04e-15      -1.13e-15      -1.20e-15
34         9.70e-17        4.23e-18       3.33e-01      -1.88e-16
35        -2.86e-18        9.48e-18      -7.06e-16      -1.54e-16
36         2.73e-17        8.90e-17      -4.48e-16      -2.23e-16
37         1.95e-16       -1.38e-17       3.60e-16      -6.83e-01
38        -1.02e-16       -1.70e-16       1.86e-17      -1.12e-16
39        -9.92e-17       -9.98e-17      -3.23e-18       4.57e-17
40        -4.25e-16       -2.47e-16      -2.39e-16      -1.31e-16
41        -2.04e-17       -1.26e-17       6.48e-17      -3.02e-17
42        -1.28e-18       -6.75e-19       1.29e-18      -4.02e-20
43        -9.00e-16       -6.40e-16      -8.86e-17      -6.70e-16
44         3.68e-16        1.23e-16      -1.48e-16       3.74e-16
45         8.80e-16        5.28e-16       2.60e-16       4.57e-16
46         1.04e+00        1.04e+00       1.04e+00       1.04e+00
47        -1.53e-16       -1.67e-16      -2.35e-17      -1.05e-16
48        -1.71e-15       -1.57e-15      -9.67e-16      -6.79e-16
49         2.37e-16        1.42e-16      -4.55e-01       2.24e-16
50        -6.10e-17       -8.67e-17       1.53e-16      -1.97e-16
51        -1.15e-16       -7.96e-17      -2.94e-16      -9.55e-17
52        -3.86e-16       -2.45e-16      -2.47e-16       4.32e-01
53         5.64e-17        2.67e-17       7.56e-17       8.84e-17
54         5.71e-17        5.42e-17       4.03e-17       3.08e-17
55        -3.98e-02       -6.67e-17      -4.75e-17      -3.61e-17
56        -8.87e-17       -6.31e-17      -1.01e-16      -1.03e-16
57         1.12e-16        9.74e-17       9.91e-18       1.26e-16
58         1.97e-16       -2.63e-01       1.44e-16       7.80e-17
59        -1.38e-17        1.09e-16       5.19e-17       4.81e-17
60         1.80e-17       -9.69e-17      -3.89e-17       2.63e-17
61        -3.59e-01       -3.59e-01       7.00e-16       9.91e-16
62        -1.84e-16       -1.84e-16      -1.32e-16      -1.25e-16
63        -6.92e-16       -8.11e-16      -7.32e-16      -8.44e-16
64        -4.13e-16       -5.40e-16      -1.68e-16      -2.66e-16
65        -8.87e-19       -8.16e-19      -1.76e-18      -1.23e-18
66        -1.74e-17        2.32e-17       2.00e-17      -2.76e-19
67         1.40e-16        1.12e-16       6.08e-17       3.42e-17
68         2.61e-17        2.68e-17       7.68e-18       1.84e-17
69        -1.19e-16       -1.22e-16      -1.78e-17      -2.04e-16
70         3.13e-01       -5.31e-17      -3.48e-16      -6.47e-17
71         8.35e-17        8.01e-17       1.66e-16       6.21e-17
72        -1.62e-17        2.81e-17       1.16e-17      -1.32e-17
73        -1.90e-16        1.75e-01      -1.61e-16      -9.57e-17
74         1.35e-17        3.77e-17      -5.04e-19       1.06e-17
75        -5.60e-18        3.08e-18       5.78e-19      -6.02e-18
76         3.91e-16        3.48e-16      -1.29e-01      -1.29e-01
77        -5.38e-16       -5.95e-16      -6.29e-16      -5.55e-16
78        -1.56e-15       -1.57e-15      -1.90e-15      -1.85e-15
79         7.37e-18        2.70e-17      -1.08e-01      -2.45e-17
80         1.47e-16        1.54e-16      -5.93e-17       3.09e-17
81         5.27e-17        4.42e-17      -4.34e-16      -1.48e-16
82        -1.50e-17       -3.21e-17       7.29e-17       2.77e-01
83        -1.86e-17       -4.42e-17      -5.03e-18      -1.10e-17
84         2.00e-17       -7.38e-17       2.16e-17       2.57e-16
85         2.56e-17       -1.97e-18       6.45e-17       3.43e-17
86        -6.14e-17       -3.37e-17      -6.66e-17      -2.77e-17
87        -3.61e-17       -1.45e-17      -7.33e-18       4.52e-18
88        -1.95e-16       -1.49e-16      -2.13e-17      -1.62e-16
89        -1.74e-16       -1.97e-16       1.43e-17      -2.06e-16
90         3.35e-16        2.71e-16       8.04e-17       2.01e-16
91        -4.75e-01       -4.75e-01      -4.75e-01      -4.75e-01
92         1.23e-15        1.17e-15       3.47e-16       1.02e-15
93         3.76e-16        3.53e-16       2.36e-16       1.25e-16
94        -5.90e-17       -5.33e-17       8.35e-02      -6.19e-17
95         4.11e-17       -3.85e-17       5.01e-16      -2.58e-16
96         1.91e-17        2.28e-17       5.98e-17       3.10e-17
97         1.13e-16        2.79e-17       2.69e-17      -3.06e-01
98        -3.48e-17       -7.85e-18      -4.79e-17      -1.01e-16
99        -4.53e-17       -4.22e-17      -3.46e-17      -4.65e-17
100       -2.64e-01       -4.63e-16      -3.29e-16      -2.03e-16
101        4.27e-16        2.02e-16       4.11e-16       3.82e-16
102        2.56e-17        1.91e-17       2.86e-17      -1.43e-17
103        5.58e-16       -5.59e-01       5.37e-16       4.32e-16
104        4.00e-18        5.12e-18       6.98e-18       2.94e-18
105       -1.37e-16       -1.37e-16      -3.67e-17       1.15e-17
106        2.83e-01        2.83e-01      -6.05e-16      -8.33e-16
107        2.13e-16        2.29e-16       2.17e-16       2.19e-16
108        5.17e-16        4.58e-16       5.49e-16       5.74e-16
109        4.07e-16        3.94e-16       2.70e-17       3.49e-16
110        7.54e-17        8.80e-17       9.35e-17       7.41e-17
111       -1.32e-16        7.68e-17       1.04e-16      -9.66e-17
112       -4.23e-16       -3.34e-16      -1.33e-16       1.59e-17
113       -3.26e-17       -5.51e-17      -2.76e-17      -3.49e-17
114        1.16e-17        1.27e-17       2.44e-17      -9.50e-18
115       -3.08e-01        3.62e-17       3.36e-16       6.83e-17
116       -7.16e-18       -1.14e-17      -2.20e-17      -1.19e-17
117        1.81e-18        1.02e-18      -5.12e-18      -6.55e-19
118        5.49e-17       -1.32e-01       7.73e-17       1.35e-17
119       -1.22e-16       -2.26e-16      -8.73e-18      -5.97e-17
120       -1.54e-18       -2.14e-18      -1.46e-17      -1.56e-17
121       -1.53e-15       -1.37e-15       5.05e-01       5.05e-01
122       -4.20e-16       -4.51e-16      -5.20e-16      -4.77e-16
123        6.36e-16        7.41e-16       8.24e-16       8.58e-16
124        6.21e-17        4.34e-17      -2.24e-01       2.09e-17
125        2.32e-17        1.63e-17      -6.31e-17       4.64e-17
126       -2.40e-16       -1.84e-16      -2.62e-16      -3.22e-16
127       -3.31e-16       -2.47e-16      -1.74e-16       3.96e-01
128       -5.03e-18        2.85e-18       1.68e-17      -2.91e-17
129        1.47e-17        1.28e-17       2.11e-18       4.26e-17
130        1.35e-16       -5.20e-17       3.89e-16       1.46e-16
131       -2.16e-17        6.99e-19      -8.05e-18      -5.74e-18
132        2.06e-17        3.72e-19       2.13e-17       1.02e-17
133        1.06e-15        8.87e-16       2.05e-17       7.92e-16
134       -3.20e-16       -2.03e-16       1.05e-16      -3.30e-16
135       -1.17e-15       -1.02e-15      -2.36e-16      -7.76e-16
    dfb.ntrgn110.b3 dfb.ntrgn140.b3 dfb.n0.2.1 dfb.n50.2.1 dfb.n80.2.1
1         -5.27e-01       -5.27e-01   5.27e-01   -3.84e-15   -4.40e-15
2          1.87e-15        2.32e-15  -5.74e-01    1.84e-15    3.46e-15
3         -2.09e-15        4.44e-16   3.21e-15    2.60e-15    3.59e-15
4          1.06e-15       -1.11e-18  -2.46e-15    3.70e-01   -1.70e-15
5         -4.46e-16       -3.04e-15  -2.42e-15   -8.10e-01   -1.99e-15
6         -1.42e-16       -4.12e-16  -1.78e-16   -6.14e-16   -2.48e-16
7          1.28e-16        4.44e-16   1.81e-16    2.60e-16   -1.24e-01
8         -1.50e-17        1.71e-17   6.58e-17    4.36e-17   -1.41e-02
9         -4.09e-17        1.15e-16   1.70e-16    1.34e-16    1.45e-16
10         3.04e-01       -1.01e-15   9.93e-16   -3.02e-16   -6.52e-17
11         8.04e-16        7.29e-16   1.79e-16    2.36e-16    4.61e-16
12         1.68e-16        1.67e-16   1.51e-16    3.41e-16    2.66e-16
13        -4.84e-16        8.39e-01   4.66e-16   -1.26e-15    8.78e-17
14         1.19e-16        2.34e-16   8.05e-17    1.29e-16    1.84e-16
15        -3.74e-18        6.51e-17   1.09e-16    1.51e-16    6.46e-17
16         2.13e-16        9.44e-17  -2.16e-16   -6.21e-17   -9.72e-17
17         9.80e-17        8.53e-17  -1.03e-16    1.08e-18   -7.88e-18
18        -5.85e-16       -6.12e-16   9.71e-16    1.38e-16    4.36e-17
19        -9.55e-19       -2.30e-16  -7.53e-17   -6.96e-17   -1.91e-16
20         9.69e-17        2.48e-17  -1.78e-16   -1.01e-16   -7.12e-17
21        -2.74e-16        9.30e-16   1.15e-15    1.58e-15    1.09e-15
22        -9.04e-16       -2.53e-17   1.24e-15    7.78e-16    8.74e-16
23        -5.51e-17        2.20e-17   1.97e-16    1.88e-16    2.02e-16
24        -2.25e-16        5.89e-17   2.53e-16    2.52e-16    7.34e-17
25        -3.18e-18       -4.41e-18  -4.13e-18   -6.95e-19   -4.87e-18
26         4.34e-16        2.54e-16  -2.90e-17   -1.36e-16    5.48e-17
27         4.23e-17        9.35e-18  -7.13e-17   -1.21e-16   -8.86e-17
28        -2.63e-17        3.15e-17   7.33e-17    7.64e-17    5.58e-17
29         3.35e-17        1.57e-16   5.23e-16    3.52e-16    4.89e-16
30         5.91e-18       -9.17e-17  -1.24e-16   -1.18e-16   -1.78e-16
31        -3.73e-01       -3.73e-01   1.33e-15    7.16e-16    5.17e-16
32        -1.82e-15       -1.81e-15   2.80e-15    1.67e-16    3.39e-16
33        -1.14e-15       -9.37e-16   1.88e-15    3.87e-16    4.44e-16
34        -1.24e-16       -4.97e-16  -2.93e-16   -5.45e-16   -4.93e-16
35        -8.06e-17       -7.93e-16  -8.04e-16   -9.71e-16   -6.75e-16
36        -1.64e-16       -1.15e-15  -1.13e-15   -1.24e-15   -1.21e-15
37         2.76e-16       -4.95e-17  -4.37e-16   -2.73e-16   -3.44e-16
38         3.69e-18       -1.20e-16   4.80e-17    4.22e-17   -4.83e-18
39        -1.14e-16       -4.06e-16  -3.86e-16   -4.48e-16   -5.56e-16
40         3.62e-01       -1.52e-16   1.42e-16   -2.09e-16    4.91e-17
41         1.16e-16       -7.95e-17  -4.14e-16   -2.72e-16   -3.71e-16
42         5.17e-19       -2.68e-19  -4.14e-19    8.22e-19   -1.29e-19
43        -7.51e-16        2.89e-01   2.89e-01    2.89e-01    2.89e-01
44         4.76e-16        1.22e-16  -3.67e-01   -3.67e-01   -3.67e-01
45         4.18e-16        1.13e-15   2.65e-16    4.24e-16   -2.22e-16
46         1.04e+00        1.04e+00  -1.04e+00   -5.29e-15   -5.67e-15
47        -1.17e-16       -1.70e-16  -8.29e-02   -1.47e-16   -2.41e-16
48        -1.55e-15        5.62e-16   2.42e-15    1.97e-15    2.64e-15
49         3.02e-16       -1.58e-16  -4.51e-16   -4.55e-01   -5.23e-16
50        -2.27e-16       -5.85e-16  -1.52e-16    2.63e-01   -2.97e-16
51        -1.86e-16       -2.87e-16  -1.35e-16   -4.00e-16   -2.39e-16
52        -2.50e-16        4.00e-16   1.10e-15    5.02e-16    4.32e-01
53         8.48e-17       -1.77e-17  -2.05e-16   -1.30e-16   -9.54e-02
54         5.42e-17       -6.17e-17  -1.37e-16   -1.04e-16   -1.09e-16
55        -3.98e-02       -4.36e-17  -2.69e-18   -2.25e-17   -1.53e-17
56        -1.18e-16       -1.20e-16   6.42e-18   -5.74e-17   -4.19e-17
57         1.00e-16        2.63e-16   1.32e-16    8.58e-17    1.83e-16
58         1.27e-16       -2.63e-01  -2.39e-16    2.72e-16   -2.02e-17
59        -1.95e-17        1.64e-16   9.50e-17    1.87e-16    1.06e-16
60         2.02e-17       -9.25e-18   5.69e-17    7.56e-17    2.69e-17
61         6.08e-16        8.23e-16  -1.92e-15   -5.71e-16   -2.97e-16
62        -1.42e-16       -1.38e-16   2.41e-16    7.37e-17    4.22e-17
63        -8.26e-16       -8.76e-16   1.40e-15    4.22e-16    1.08e-16
64        -1.17e-16        2.76e-16   1.94e-15    1.13e-15    4.20e-16
65        -1.36e-18       -3.76e-19   2.86e-18    1.40e-18    1.77e-18
66        -3.65e-17        2.54e-17   7.55e-17    7.79e-17    4.49e-17
67         1.04e-16       -6.64e-18  -5.53e-17   -5.52e-17   -4.05e-17
68         1.75e-17        3.49e-17   1.61e-17    2.98e-17    4.28e-17
69        -1.59e-16       -5.72e-17   1.12e-16    5.99e-17   -1.58e-17
70        -5.67e-17       -1.57e-16   9.87e-17   -3.56e-16   -1.35e-16
71         2.46e-16        1.35e-16  -1.02e-16    2.90e-17   -7.72e-17
72        -1.10e-17       -4.37e-17  -6.39e-17   -1.17e-17   -5.00e-17
73        -1.28e-16        1.32e-17   2.67e-16    1.14e-16    1.77e-16
74         9.71e-19       -3.38e-18  -2.88e-17   -3.62e-17   -1.86e-17
75        -3.81e-18       -9.33e-18  -2.49e-17   -2.52e-17   -3.28e-17
76        -1.29e-01       -1.29e-01  -6.38e-16   -6.04e-17   -1.61e-16
77        -5.93e-16       -6.15e-16   8.62e-16    1.03e-16    6.31e-17
78        -2.19e-15       -1.82e-15   2.82e-15    7.86e-16    5.43e-16
79        -4.51e-17       -6.65e-17  -1.77e-16   -9.69e-17   -6.73e-17
80         1.11e-16       -2.47e-17  -2.59e-16   -2.80e-17   -8.92e-17
81        -3.54e-16       -1.14e-15  -1.90e-15   -1.73e-15   -1.14e-15
82         6.07e-17       -1.03e-16  -2.67e-16   -2.54e-16   -3.33e-16
83        -3.12e-18       -3.90e-17   6.56e-17    5.37e-17    3.40e-17
84        -1.17e-17       -3.46e-16  -2.62e-16   -3.07e-16   -2.70e-16
85        -3.98e-02       -6.10e-18  -4.70e-17    9.39e-18   -2.03e-17
86        -2.28e-17       -5.77e-17  -1.25e-16   -2.15e-16   -1.73e-16
87        -5.04e-18        2.02e-17   3.03e-17    8.18e-19    1.96e-17
88        -1.61e-16        6.44e-02   6.44e-02    6.44e-02    6.44e-02
89        -1.83e-16       -2.21e-16   1.21e-01    1.21e-01    1.21e-01
90         1.51e-16        2.06e-16  -5.76e-17    5.36e-17   -1.41e-16
91        -4.75e-01       -4.75e-01   4.75e-01    1.98e-15    2.16e-15
92         1.02e-15        1.28e-15   6.61e-01    1.60e-15    2.51e-15
93         3.69e-16        2.35e-17  -4.54e-16   -3.48e-16   -4.77e-16
94        -1.00e-16        2.11e-17   2.10e-16    8.35e-02    1.87e-16
95        -3.03e-16       -1.11e-15  -6.80e-16    5.31e-01   -8.16e-16
96        -1.01e-18        5.98e-17   5.22e-17    1.05e-16    6.86e-17
97         3.57e-17       -2.22e-16  -5.40e-16   -2.39e-16   -3.06e-01
98        -3.02e-17        9.43e-17   2.49e-16    1.66e-16    1.09e-01
99        -4.03e-17        1.14e-16   1.62e-16    1.29e-16    1.13e-16
100       -2.64e-01       -2.85e-16   8.81e-17   -4.52e-17    4.04e-17
101        5.76e-16        4.80e-16   9.01e-17    3.46e-16    2.80e-16
102       -4.45e-19       -1.76e-17  -3.75e-17   -9.20e-19   -3.69e-17
103        5.37e-16       -5.59e-01  -5.28e-16    5.58e-16    5.92e-17
104        4.98e-18        1.30e-17   1.39e-18    1.35e-17    1.15e-18
105       -9.87e-17        9.81e-17   1.75e-16    3.88e-17    2.05e-16
106       -4.25e-16       -6.00e-16   1.32e-15    2.92e-16    1.16e-16
107        1.87e-16        2.05e-16  -2.03e-16    2.61e-17    5.72e-17
108        4.93e-16        4.26e-16  -6.27e-16   -4.76e-17    6.38e-17
109        2.24e-16       -3.29e-16  -1.62e-15   -1.06e-15   -1.30e-16
110        8.32e-17        3.46e-17  -9.99e-17   -1.53e-17   -6.07e-17
111       -1.86e-16        3.95e-16   5.86e-16    5.79e-16    4.31e-16
112       -2.63e-16        2.53e-16   3.13e-16    4.42e-16    4.49e-16
113       -2.54e-17       -2.26e-17   5.03e-17    5.01e-17    5.15e-17
114       -2.55e-17        4.27e-17   7.44e-17    9.29e-17    7.72e-17
115        9.13e-17        2.12e-16   1.38e-17    4.96e-16    2.33e-16
116       -2.36e-17       -2.24e-17   5.54e-18   -1.33e-17   -3.55e-18
117       -9.69e-19        6.83e-18   8.91e-18    2.11e-18    5.61e-18
118        4.01e-17       -5.84e-17  -1.61e-16   -7.09e-17   -1.50e-16
119       -8.83e-17        9.66e-17   3.48e-16    3.45e-16    2.67e-16
120       -7.93e-18       -5.08e-17  -4.42e-17   -7.02e-17   -6.82e-17
121        5.05e-01        5.05e-01   2.26e-15   -6.83e-17    3.13e-16
122       -4.61e-16       -4.77e-16   5.39e-16    1.19e-18   -2.82e-17
123        7.46e-16        4.06e-16  -1.42e-15   -4.12e-16   -3.49e-16
124        2.55e-17       -9.14e-17  -3.60e-16   -1.97e-16   -1.66e-16
125        7.74e-17       -1.27e-16  -2.51e-16   -2.49e-16   -2.12e-16
126       -2.59e-16       -1.44e-18   5.93e-16    3.93e-16    2.30e-16
127       -1.96e-16       -2.67e-16  -7.44e-17   -2.93e-16   -4.27e-16
128        2.49e-17        1.74e-17   5.32e-17    4.76e-17    4.32e-17
129        2.90e-17        6.12e-17   3.24e-17    5.46e-17    6.24e-17
130       -3.22e-01       -3.31e-17  -3.17e-16    1.28e-16   -1.54e-16
131        4.20e-17        2.92e-17   2.72e-17    4.67e-18    1.57e-17
132       -3.22e-18       -1.78e-18  -1.11e-17    2.60e-17    1.46e-18
133        7.84e-16       -3.55e-01  -3.55e-01   -3.55e-01   -3.55e-01
134       -3.57e-16       -2.18e-16   2.45e-01    2.45e-01    2.45e-01
135       -4.95e-16       -7.01e-16   3.74e-16    3.06e-16    1.06e-15
    dfb.n110.2.1 dfb.n140.2.1 dfb.n0.3.1 dfb.n50.3.1 dfb.n80.3.1 dfb.n110.3.1
1      -5.07e-15    -4.15e-15   5.27e-01   -3.51e-15   -4.37e-15    -4.64e-15
2       3.72e-15     3.70e-15  -9.67e-16   -2.63e-15   -4.00e-16    -1.75e-16
3       2.00e-15     2.04e-15  -3.94e-01    4.97e-15    5.99e-15     4.41e-15
4      -1.52e-15    -1.13e-15  -1.70e-15    3.70e-01   -1.33e-15    -1.21e-15
5      -1.84e-15    -3.25e-15  -3.44e-15   -1.24e-15   -3.28e-15    -3.13e-15
6      -2.52e-16    -2.68e-16  -5.53e-16   -1.57e-01   -5.89e-16    -6.16e-16
7       3.16e-16     3.68e-16   2.78e-16    3.03e-16   -1.24e-01     3.89e-16
8       4.64e-17     5.26e-17   5.00e-17    3.69e-17    3.95e-17     4.11e-17
9       1.37e-16     1.42e-16   3.09e-16    2.85e-16   -3.60e-02     2.83e-16
10      3.04e-01    -2.73e-17   3.50e-16   -3.71e-16   -8.07e-17     3.04e-01
11     -2.57e-01     5.10e-16  -1.88e-16   -7.45e-17    1.72e-16     3.91e-16
12      3.48e-16     1.77e-16   2.34e-16    3.57e-16    1.87e-16     2.16e-01
13     -1.81e-16     8.39e-01  -1.12e-15   -8.46e-16    2.38e-18    -3.28e-16
14      2.25e-16     2.76e-01   1.91e-16    1.71e-16    1.94e-16     1.83e-16
15      6.26e-17     1.35e-16  -2.91e-17    4.92e-17    4.44e-17    -2.99e-18
16     -2.26e-17    -9.47e-17  -2.48e-16   -5.66e-17   -1.01e-16    -6.36e-18
17      9.06e-18    -3.26e-18  -7.65e-17   -1.09e-17   -7.43e-18     1.07e-17
18      8.54e-17     1.17e-16   6.23e-16    8.08e-17   -1.51e-17    -1.03e-17
19     -1.78e-16    -2.22e-16  -3.61e-16   -3.15e-16   -2.88e-16    -2.71e-16
20     -1.11e-16    -8.86e-17  -1.93e-16   -1.44e-16   -1.17e-16    -1.01e-16
21      1.00e-15     1.28e-15   1.34e-15    1.92e-15    1.30e-15     1.03e-15
22      3.68e-16     7.23e-16   6.60e-16    8.94e-16    9.34e-16     4.44e-16
23      2.01e-16     1.25e-16   2.59e-16    2.15e-16    2.53e-16     2.37e-16
24      1.42e-16     1.86e-16   6.64e-16    6.12e-16    4.06e-16     3.28e-16
25     -5.51e-18    -3.15e-18  -1.65e-18    1.93e-18   -3.09e-18    -2.68e-18
26      7.58e-17     1.15e-16  -2.34e-16   -2.24e-16   -1.93e-18     3.98e-17
27     -7.24e-17    -5.89e-17  -1.24e-16   -9.56e-17   -4.67e-17    -5.77e-17
28      5.92e-17     6.64e-17   9.85e-17    8.86e-17    8.04e-17     7.70e-17
29      4.49e-16     3.53e-16   1.35e-16    1.95e-16    2.57e-16     2.35e-16
30     -1.56e-16    -1.68e-16  -1.27e-16   -1.04e-16   -1.59e-16    -1.13e-16
31      3.58e-16     4.42e-16   9.50e-16    1.90e-16    1.42e-16     4.55e-17
32      3.44e-16     7.47e-17   2.17e-15    4.78e-16    4.66e-16     2.92e-16
33      3.40e-16     4.08e-16   1.30e-15    3.95e-16    3.65e-16     2.18e-16
34     -4.92e-16    -4.95e-16  -5.87e-16   -7.54e-16   -5.15e-16    -4.64e-16
35     -8.13e-16    -7.90e-16  -1.12e-15   -1.53e-15   -1.02e-15    -9.41e-16
36     -1.17e-15    -1.19e-15  -1.54e-15   -1.94e-15   -1.59e-15    -1.49e-15
37     -3.49e-16    -3.07e-16  -2.39e-16   -3.50e-16   -5.13e-16    -2.91e-16
38      2.61e-17     8.87e-18  -3.98e-16   -3.78e-16   -4.53e-16    -3.78e-16
39     -5.11e-16    -4.90e-16  -5.55e-16   -5.95e-16   -6.66e-16    -5.87e-16
40     -8.07e-18     3.86e-17  -2.31e-16   -6.23e-16   -4.33e-16    -4.80e-16
41     -3.34e-16    -3.61e-16   1.37e-16    1.20e-16    6.19e-17     6.48e-17
42     -5.39e-19    -4.88e-19  -1.01e-19   -2.22e-19   -1.06e-18    -1.38e-18
43      2.89e-01     2.89e-01   2.89e-01    2.89e-01    2.89e-01     2.89e-01
44     -3.67e-01    -3.67e-01  -8.01e-16   -8.23e-16   -5.33e-16    -2.60e-16
45      4.73e-16     5.50e-16  -5.82e-01   -5.82e-01   -5.82e-01    -5.82e-01
46     -3.01e-15    -5.00e-15  -1.04e+00   -5.19e-15   -5.23e-15    -3.04e-15
47     -2.41e-16    -2.56e-16   9.81e-18    1.86e-16    2.45e-17     3.75e-18
48      1.57e-15     1.55e-15   5.10e-01    3.24e-15    4.22e-15     3.13e-15
49     -8.41e-16    -5.01e-16  -1.00e-15   -4.55e-01   -5.40e-16    -8.85e-16
50     -2.85e-16    -4.92e-16  -4.31e-16   -7.02e-17   -4.88e-16    -4.97e-16
51     -2.12e-16    -1.88e-16  -3.94e-16    2.21e-01   -5.09e-16    -5.10e-16
52      5.75e-16     6.25e-16   1.73e-15    6.79e-16    4.32e-01     7.86e-16
53     -1.28e-16    -1.54e-16  -1.92e-16   -1.14e-16   -1.33e-16    -1.24e-16
54     -9.86e-17    -1.00e-16  -2.53e-16   -2.02e-16   -4.71e-02    -2.13e-16
55     -3.98e-02    -6.70e-18   6.64e-17   -1.23e-17    0.00e+00    -3.98e-02
56     -7.39e-02    -4.60e-17   2.48e-17   -3.82e-17   -2.11e-17    -3.57e-17
57      2.67e-16     1.75e-16   1.44e-16    2.19e-17    1.77e-16    -3.14e-01
58      0.00e+00    -2.63e-01   9.45e-17    4.27e-17   -2.52e-17    -2.34e-17
59      6.97e-17    -2.52e-01   7.67e-17    9.07e-17    7.96e-17     3.20e-17
60      2.55e-17     3.61e-17   1.53e-16    1.13e-16    1.35e-16     1.30e-16
61     -6.31e-16    -2.17e-16  -8.27e-16   -7.19e-16   -2.47e-16    -5.64e-16
62      1.66e-17     2.08e-17   1.28e-16    7.56e-17    3.91e-17    -1.74e-18
63      1.63e-16     1.45e-16   5.28e-16    3.40e-16   -1.19e-16    -2.21e-17
64      7.35e-16     6.47e-16   1.19e-15    1.09e-15    7.77e-16     9.48e-16
65      1.19e-18     1.33e-18   2.09e-18    1.53e-18    1.49e-18     8.52e-19
66      2.76e-17     4.68e-17   9.02e-17    1.46e-16    7.79e-17     5.10e-17
67     -1.94e-17    -4.03e-17  -3.90e-16   -1.41e-16   -1.62e-16    -8.03e-17
68      4.29e-17     3.85e-17   2.29e-18    3.74e-17    3.85e-17     3.32e-17
69      7.23e-17     7.66e-17   5.99e-17    5.98e-17   -7.09e-17     1.24e-17
70     -9.14e-17    -1.30e-16   5.10e-17   -2.09e-16   -3.74e-17     1.14e-17
71      4.11e-17    -7.71e-18  -1.23e-16    1.44e-17   -8.67e-17    -6.67e-18
72     -1.53e-17    -1.70e-17  -3.45e-17    2.62e-17   -5.71e-18     1.75e-17
73      1.10e-16     1.29e-16   2.78e-16    1.18e-16    1.60e-16     1.31e-16
74     -2.23e-17    -1.78e-17  -1.06e-17   -3.15e-18   -1.37e-17    -3.18e-18
75     -2.88e-17    -2.62e-17  -1.79e-17   -1.56e-17   -2.56e-17    -2.07e-17
76     -1.46e-16    -7.72e-17  -3.28e-16   -1.93e-16   -2.10e-16    -1.12e-16
77     -1.50e-17     4.04e-18   4.64e-16    2.69e-16    1.48e-16     4.22e-17
78      1.90e-16     3.05e-16   1.24e-15    7.54e-16    3.50e-16    -1.80e-17
79     -8.09e-17    -6.90e-17  -9.28e-17   -1.27e-16   -1.02e-16    -8.84e-17
80      5.57e-18     8.65e-18  -3.52e-16   -3.46e-16   -2.88e-16    -2.38e-16
81     -1.47e-15    -1.20e-15  -1.69e-15   -2.19e-15   -1.39e-15    -1.54e-15
82     -2.63e-16    -3.16e-16  -3.98e-16   -1.96e-16   -2.19e-16    -1.76e-16
83      3.15e-17     2.57e-17  -8.79e-17   -1.10e-16   -1.10e-16    -1.04e-16
84     -2.41e-16    -3.28e-16  -5.46e-16   -5.55e-16   -5.26e-16    -4.91e-16
85     -2.24e-17    -3.46e-17  -4.36e-17   -1.22e-17   -3.50e-17    -3.78e-17
86     -1.80e-16    -1.94e-16   3.02e-17   -6.23e-17   -2.65e-17    -2.57e-17
87      1.30e-17     7.62e-19   1.58e-17   -1.73e-17    3.75e-18    -2.17e-18
88      6.44e-02     6.44e-02   6.44e-02    6.44e-02    6.44e-02     6.44e-02
89      1.21e-01     1.21e-01   2.01e-16    1.33e-16    6.61e-18    -3.08e-17
90     -2.04e-17     2.43e-17  -1.69e-01   -1.69e-01   -1.69e-01    -1.69e-01
91      1.17e-15     2.02e-15   4.75e-01    1.67e-15    1.86e-15     1.11e-15
92      2.34e-15     2.34e-15  -3.57e-16   -1.21e-15   -2.13e-16    -2.38e-16
93     -2.07e-16    -2.14e-16  -1.13e-01   -6.83e-16   -8.21e-16    -5.47e-16
94      2.32e-16     1.68e-16   2.10e-16    8.35e-02    1.30e-16     1.79e-16
95     -6.86e-16    -1.13e-15  -9.81e-16   -3.18e-16   -1.05e-15    -9.81e-16
96      4.19e-17     4.10e-17   1.06e-16   -6.39e-02    1.45e-16     1.17e-16
97     -2.75e-16    -2.98e-16  -8.03e-16   -2.35e-16   -3.06e-01    -3.68e-16
98      2.04e-16     2.11e-16   2.62e-16    1.58e-16    1.76e-16     1.85e-16
99      1.16e-16     1.36e-16   3.59e-16    2.81e-16    8.32e-02     2.83e-16
100    -2.64e-01     6.55e-17   4.35e-16   -1.27e-16   -1.87e-17    -2.64e-01
101     3.32e-01     2.55e-16  -7.58e-17    1.11e-16    8.94e-17     1.64e-16
102    -3.22e-17    -2.69e-17  -2.22e-17    2.21e-17   -3.43e-17     9.68e-02
103     9.45e-17    -5.59e-01   1.67e-16    2.11e-16   -2.30e-17     7.93e-17
104     4.86e-18    -2.43e-02   8.76e-18    8.88e-18    6.96e-18     7.05e-18
105     1.94e-16     2.01e-16   2.72e-16    1.92e-16    2.48e-16     2.22e-16
106     4.95e-16     1.03e-16   6.61e-16    2.47e-16    6.85e-17     4.20e-16
107     2.50e-17     2.93e-17  -1.57e-16    5.76e-17    5.41e-17     4.03e-17
108    -3.74e-17    -9.48e-17  -4.68e-16    4.48e-17    3.87e-17    -1.19e-17
109    -6.29e-16    -6.14e-16  -1.24e-15   -1.09e-15   -6.43e-16    -8.68e-16
110    -5.88e-17    -4.33e-17  -1.15e-16   -4.79e-17   -5.68e-17    -6.00e-17
111     5.67e-16     6.09e-16   8.08e-16    9.58e-16    5.71e-16     6.64e-16
112     2.62e-16     3.89e-16   1.59e-15    7.16e-16    9.90e-16     5.60e-16
113     3.76e-17     2.19e-17   3.19e-17    4.97e-17    5.30e-17     4.69e-17
114     8.12e-17     8.33e-17   6.62e-17    1.14e-16    1.07e-16     9.92e-17
115     2.37e-16     2.12e-16   8.08e-17    4.06e-16    1.54e-16     1.56e-16
116    -9.54e-18    -6.62e-18   9.58e-18   -7.68e-18   -7.38e-19    -4.01e-18
117     5.30e-18     4.63e-18   1.19e-17    4.17e-18    9.42e-18     7.16e-18
118    -9.33e-17    -9.11e-17  -2.03e-16   -1.32e-16   -1.66e-16    -1.40e-16
119     2.65e-16     2.58e-16   1.67e-16    1.52e-16    1.79e-16     1.08e-16
120    -5.39e-17    -6.85e-17  -3.72e-17   -4.85e-17   -5.98e-17    -3.23e-17
121     5.52e-16     2.22e-16   1.25e-15    1.78e-17    2.90e-16     1.58e-16
122    -2.74e-17    -4.35e-18   3.45e-16   -9.24e-17   -8.31e-17    -6.47e-17
123    -4.12e-16    -3.62e-16  -9.98e-16   -1.89e-16   -2.40e-16    -2.53e-16
124    -1.84e-16    -1.93e-16  -1.87e-16   -2.04e-16   -1.88e-16    -1.59e-16
125    -2.27e-16    -2.15e-16  -2.62e-16   -3.24e-16   -2.09e-16    -1.90e-16
126     3.89e-16     3.50e-16   6.01e-16    5.12e-16    2.40e-16     3.85e-16
127    -2.79e-16    -3.17e-16  -2.05e-18   -8.22e-17   -2.11e-16    -1.14e-16
128     4.40e-17     5.68e-17  -5.80e-17   -7.30e-17   -9.40e-17    -7.59e-17
129     5.62e-17     5.14e-17   1.85e-17    5.22e-17    8.28e-17     5.81e-17
130    -1.74e-16    -1.59e-16  -2.11e-16    1.25e-16   -1.22e-16    -1.58e-16
131     3.10e-17     2.55e-17   1.02e-17   -9.44e-18    4.63e-18     1.20e-17
132     1.46e-18    -1.21e-17   4.73e-17    7.87e-17    5.36e-17     6.01e-17
133    -3.55e-01    -3.55e-01  -3.55e-01   -3.55e-01   -3.55e-01    -3.55e-01
134     2.45e-01     2.45e-01   4.47e-16    3.56e-16    1.40e-16     4.10e-17
135     4.45e-16     1.73e-16   7.61e-01    7.61e-01    7.61e-01     7.61e-01
    dfb.n140.3.1 dfb.n0.2.2 dfb.n50.2.2 dfb.n80.2.2 dfb.n110.2.2 dfb.n140.2.2
1      -4.04e-15  -5.29e-15   -3.87e-15   -3.90e-15    -3.85e-15    -3.88e-15
2      -2.34e-16   4.28e-15    1.95e-15    2.56e-15     2.64e-15     2.70e-15
3       4.35e-15   2.10e-15    2.87e-15    3.71e-15     2.82e-15     2.81e-15
4      -8.32e-16  -1.88e-15   -1.33e-15   -1.51e-15    -2.36e-15    -1.66e-15
5      -4.39e-15  -2.32e-15   -3.11e-15   -2.00e-15    -1.72e-15    -2.45e-15
6      -6.22e-16  -2.45e-16   -2.43e-16   -2.69e-16    -2.23e-16    -2.70e-16
7       4.70e-16   3.44e-16    3.43e-16    3.14e-16     2.83e-16     3.11e-16
8       4.19e-17   5.23e-17    5.50e-17    4.78e-17     4.92e-17     4.83e-17
9       2.94e-16   1.23e-16    1.43e-16    1.38e-16     1.34e-16     1.39e-16
10     -8.41e-17  -6.07e-16   -4.74e-17   -2.78e-16    -9.28e-18    -6.80e-17
11      2.40e-16   5.51e-16    4.30e-16    4.60e-16     4.09e-16     4.15e-16
12      2.07e-16   2.37e-16    2.45e-16    2.01e-16     1.93e-16     2.23e-16
13      8.39e-01  -3.79e-16   -4.09e-16   -9.29e-17    -2.63e-16    -6.40e-16
14      2.29e-16   2.10e-16    1.94e-16    1.72e-16     2.22e-16     2.19e-16
15     -1.68e-01   6.86e-17    7.04e-17    4.38e-17     4.50e-17     1.83e-17
16     -6.51e-17   7.45e-02   -3.73e-17   -1.39e-16    -9.21e-17    -1.14e-16
17     -1.50e-18  -2.32e-02    7.72e-18   -3.67e-19    -3.20e-18    -2.23e-18
18      1.57e-17  -2.43e-17    7.84e-17    1.69e-16     1.72e-16     1.00e-16
19     -3.44e-16  -1.61e-16   -1.30e-01   -1.98e-16    -2.32e-16    -2.28e-16
20     -1.23e-16  -1.01e-16    9.86e-02   -7.83e-17    -9.94e-17    -1.16e-16
21      1.41e-15   1.39e-15    1.34e-15    1.27e-15     1.36e-15     1.03e-15
22      8.03e-16   3.03e-16    9.77e-16   -5.69e-01     7.95e-16     9.68e-16
23      1.23e-16   1.79e-16    2.55e-16    1.62e-01     1.61e-16     1.78e-16
24      4.68e-16   1.27e-16    1.38e-16    1.01e-16     2.28e-16     1.37e-16
25     -1.76e-18  -4.53e-18   -4.46e-18   -2.81e-18     4.70e-03    -4.14e-18
26     -3.81e-17   2.54e-17    1.09e-17    6.78e-18    -2.16e-01    -7.01e-18
27     -3.55e-17  -7.13e-17   -7.11e-17   -9.31e-17    -1.27e-16    -8.33e-17
28      7.71e-17   6.71e-17    6.77e-17    5.49e-17     6.90e-17     4.34e-02
29      2.16e-16   3.77e-16    4.61e-16    4.35e-16     4.35e-16    -3.70e-01
30     -1.07e-16  -1.56e-16   -1.39e-16   -1.30e-16    -1.39e-16    -1.83e-16
31     -2.98e-17   4.61e-16    6.64e-16    5.58e-16     2.74e-16     6.08e-16
32      1.02e-16   1.81e-16    1.67e-16    4.00e-16     2.71e-16     2.24e-16
33      2.97e-16   3.79e-16    2.48e-16    4.94e-16     4.28e-16     3.29e-16
34     -5.86e-16  -6.01e-16   -6.19e-16   -4.90e-16    -6.06e-16    -5.33e-16
35     -1.01e-15  -9.97e-16   -7.55e-16   -8.03e-16    -9.33e-16    -9.51e-16
36     -1.55e-15  -1.31e-15   -1.05e-15   -9.92e-16    -1.33e-15    -1.42e-15
37     -4.60e-16  -7.67e-17    1.58e-16   -3.06e-16    -3.45e-16    -1.76e-16
38     -4.32e-16  -1.11e-16    8.30e-17    1.98e-17     5.59e-17     8.84e-17
39     -6.10e-16  -4.60e-16   -5.58e-16   -4.73e-16    -4.62e-16    -4.74e-16
40     -3.83e-16  -1.74e-16    8.21e-17   -1.22e-16     2.55e-16     3.00e-17
41      7.73e-17  -4.04e-16   -3.29e-16   -3.59e-16    -4.28e-16    -3.97e-16
42     -1.08e-18  -9.14e-19   -5.31e-19   -3.36e-19    -6.64e-19    -6.02e-19
43      2.89e-01   2.89e-01    2.89e-01    2.89e-01     2.89e-01     2.89e-01
44     -3.69e-16  -3.67e-01   -3.67e-01   -3.67e-01    -3.67e-01    -3.67e-01
45     -5.82e-01   3.25e-16    4.55e-16    5.05e-16     6.87e-17     5.97e-16
46     -4.17e-15  -5.51e-15   -4.22e-15   -4.83e-15    -3.71e-15    -4.20e-15
47     -1.41e-17  -3.09e-16   -1.28e-16   -1.82e-16    -1.73e-16    -1.84e-16
48      3.10e-15   1.67e-15    2.13e-15    2.74e-15     2.08e-15     2.03e-15
49     -5.01e-16  -1.04e-15   -6.49e-16   -7.72e-16    -1.23e-15    -7.15e-16
50     -6.96e-16  -3.52e-16   -4.43e-16   -2.80e-16    -2.62e-16    -4.44e-16
51     -4.59e-16  -1.90e-16   -1.47e-16   -1.92e-16    -1.49e-16    -1.82e-16
52      9.25e-16   5.81e-16    7.65e-16    6.47e-16     6.36e-16     6.67e-16
53     -1.29e-16  -1.63e-16   -1.64e-16   -1.13e-16    -1.42e-16    -1.35e-16
54     -2.01e-16  -8.89e-17   -1.01e-16   -1.11e-16    -1.14e-16    -1.05e-16
55      1.63e-18  -6.30e-17   -1.66e-17   -1.26e-17    -3.13e-17    -2.16e-17
56     -3.19e-17  -6.07e-17   -4.81e-17   -4.41e-17    -3.90e-17    -5.40e-17
57      2.19e-16   1.92e-16    1.50e-16    1.39e-16     1.72e-16     1.93e-16
58     -2.63e-01  -6.81e-17   -2.78e-17   -1.04e-16    -9.50e-17    -1.55e-17
59      1.43e-16   1.19e-16    1.21e-16    1.06e-16     1.18e-16     1.17e-16
60     -2.92e-01  -3.83e-17    8.92e-18   -2.18e-17    -2.74e-17     9.71e-17
61     -2.69e-16  -3.59e-01   -2.74e-16   -2.18e-16    -2.34e-16    -2.02e-16
62      4.55e-18  -8.55e-02    3.12e-17    4.38e-17     3.75e-17     3.13e-17
63     -1.36e-16   2.04e-16    7.13e-17    2.01e-16     1.38e-16     2.08e-16
64      9.39e-16   7.00e-16   -6.94e-01    6.60e-16     7.33e-16     7.32e-16
65      1.26e-18   1.59e-18    1.73e-03    1.07e-18     1.34e-18     1.47e-18
66      7.59e-17   6.37e-17   -5.11e-18    4.41e-17     6.29e-17     3.37e-17
67     -1.28e-16  -1.45e-17   -3.68e-17   -1.68e-01    -9.43e-17    -5.93e-17
68      2.97e-17   5.02e-17    3.81e-17   -8.71e-02     4.00e-17     4.81e-17
69      2.86e-17  -6.28e-18    2.03e-17   -2.04e-17     3.61e-17     7.09e-17
70     -5.93e-17  -1.67e-18   -1.39e-16   -1.38e-16    -3.13e-01    -1.43e-16
71     -4.14e-17  -3.57e-17   -4.32e-17   -8.14e-17     2.35e-01    -2.44e-17
72      1.59e-19  -2.85e-17   -5.24e-17   -4.75e-17     3.26e-17    -5.09e-17
73      1.75e-16   8.93e-17    1.28e-16    1.32e-16     1.51e-16    -1.75e-01
74     -3.11e-18  -2.04e-17   -2.11e-17   -2.20e-17    -2.22e-17    -4.98e-02
75     -1.61e-17  -2.73e-17   -2.90e-17   -2.89e-17    -2.01e-17    -2.41e-17
76     -9.91e-17  -9.61e-17   -1.80e-17   -9.89e-17    -1.48e-16    -9.78e-17
77     -5.91e-17  -5.47e-17    2.37e-17    4.67e-17    -4.61e-17    -3.66e-17
78     -2.46e-17   4.52e-16    4.07e-16    4.72e-16     4.13e-16     3.96e-16
79     -9.37e-17  -6.83e-17   -5.47e-17   -6.38e-17    -8.52e-17    -8.74e-17
80     -2.64e-16  -2.65e-17   -5.39e-17    5.24e-18     2.01e-17    -1.01e-17
81     -1.57e-15  -1.58e-15   -1.20e-15   -1.16e-15    -1.42e-15    -1.18e-15
82     -2.31e-16  -3.61e-16   -4.46e-16   -2.37e-16    -2.04e-16    -2.39e-16
83     -1.19e-16   7.49e-17    1.60e-17    1.60e-17     3.54e-17     6.13e-17
84     -5.78e-16  -3.39e-16   -1.81e-17   -3.50e-16    -3.85e-16    -3.18e-16
85     -4.07e-17  -2.93e-17   -2.96e-17   -3.23e-17    -5.34e-17    -2.12e-17
86      1.01e-17  -1.78e-16   -1.52e-16   -1.18e-16    -1.29e-16    -1.60e-16
87      1.13e-18  -2.15e-18    3.04e-17    3.03e-17     4.04e-17     1.11e-17
88      6.44e-02   6.44e-02    6.44e-02    6.44e-02     6.44e-02     6.44e-02
89     -3.17e-17   1.21e-01    1.21e-01    1.21e-01     1.21e-01     1.21e-01
90     -1.69e-01   1.04e-17    3.17e-17    1.38e-17    -1.29e-16    -1.18e-17
91      1.70e-15   2.25e-15    1.72e-15    2.02e-15     1.52e-15     1.68e-15
92     -3.48e-16   2.70e-15    1.36e-15    1.78e-15     1.63e-15     1.68e-15
93     -5.48e-16  -2.35e-16   -3.32e-16   -4.38e-16    -3.12e-16    -2.94e-16
94      1.05e-16   2.67e-16    1.95e-16    2.08e-16     3.01e-16     2.13e-16
95     -1.45e-15  -7.92e-16   -1.05e-15   -7.27e-16    -6.93e-16    -1.09e-15
96      1.20e-16   4.24e-17    3.03e-17    4.30e-17     3.33e-17     2.95e-17
97     -3.98e-16  -3.02e-16   -3.70e-16   -2.66e-16    -2.98e-16    -2.82e-16
98      1.81e-16   2.10e-16    2.26e-16    1.95e-16     1.98e-16     1.91e-16
99      2.91e-16   1.22e-16    1.18e-16    1.32e-16     1.29e-16     1.39e-16
100    -1.07e-18  -3.55e-16   -5.37e-18    5.41e-17    -9.68e-17    -2.29e-17
101     9.85e-17   3.44e-16    2.96e-16    2.94e-16     2.94e-16     3.32e-16
102    -2.30e-17  -2.17e-17   -2.30e-17   -2.44e-17    -3.51e-17    -3.87e-17
103    -5.59e-01   2.59e-17    1.12e-16   -3.85e-17    -3.37e-17     1.17e-16
104     9.00e-18   3.73e-18    5.84e-18    5.36e-18     1.82e-18     7.21e-18
105     4.64e-01   1.91e-16    1.63e-16    2.23e-16     1.73e-16     1.64e-16
106     1.62e-16   2.83e-01    2.07e-16    1.53e-16     2.03e-16     2.04e-16
107     2.51e-17   1.09e-01    1.94e-17   -3.37e-18     2.11e-17     1.96e-17
108    -6.86e-17   2.79e-17   -2.82e-17   -1.15e-16    -8.79e-17    -5.55e-17
109    -9.74e-16  -7.50e-16    8.34e-01   -6.10e-16    -6.77e-16    -6.51e-16
110    -6.15e-17  -3.27e-17   -1.00e-01   -3.29e-17    -5.19e-17    -6.35e-17
111     7.15e-16   6.27e-16    4.31e-16    6.28e-16     6.64e-16     5.15e-16
112     7.18e-16   3.35e-16    1.98e-16    7.47e-01     5.55e-16     3.67e-16
113     2.11e-17   1.29e-17    4.30e-17   -7.45e-02     3.47e-17     5.32e-17
114     9.78e-17   8.65e-17    7.56e-17    9.69e-17     6.03e-17     6.29e-17
115     1.55e-16   2.10e-16    2.54e-16    2.62e-16     3.08e-01     2.90e-16
116    -1.86e-18  -8.04e-18   -5.41e-18   -4.30e-18    -1.95e-02    -8.46e-18
117     9.61e-18   7.19e-18    7.87e-18    7.61e-18     8.99e-19     5.39e-18
118    -1.59e-16  -8.77e-17   -8.92e-17   -1.02e-16    -1.01e-16     1.32e-01
119     1.30e-16   3.94e-16    3.00e-16    3.45e-16     3.75e-16     4.21e-01
120    -4.86e-17  -6.36e-17   -5.60e-17   -5.91e-17    -5.84e-17    -6.54e-17
121     2.41e-16   2.90e-16   -1.48e-17    3.86e-16     5.44e-16     2.82e-16
122    -8.77e-17  -5.85e-17    4.24e-17    2.01e-17    -7.06e-17     3.46e-18
123    -2.72e-16  -4.94e-16   -3.82e-16   -4.86e-16    -3.62e-16    -5.20e-16
124    -1.69e-16  -1.91e-16   -1.01e-16   -1.52e-16    -2.39e-16    -2.07e-16
125    -2.15e-16  -2.76e-16   -2.02e-16   -2.11e-16    -2.22e-16    -2.26e-16
126     4.05e-16   4.62e-16    3.37e-16    3.46e-16     4.37e-16     3.76e-16
127    -1.15e-16  -4.52e-16   -5.06e-16   -2.16e-16    -1.35e-16    -2.56e-16
128    -5.87e-17   7.60e-17    4.43e-17    4.65e-17     4.62e-17     5.71e-17
129     5.82e-17   6.11e-17   -3.24e-18    5.97e-17     6.38e-17     5.63e-17
130    -1.62e-16  -2.27e-16   -2.11e-16   -2.28e-16    -4.11e-16    -1.18e-16
131     1.70e-17   3.27e-18    3.33e-17    5.24e-17     4.32e-17     1.32e-17
132     3.77e-17   1.48e-17   -1.79e-17   -7.53e-18    -7.00e-20     8.63e-18
133    -3.55e-01  -3.55e-01   -3.55e-01   -3.55e-01    -3.55e-01    -3.55e-01
134     1.02e-16   2.45e-01    2.45e-01    2.45e-01     2.45e-01     2.45e-01
135     7.61e-01   3.23e-16    2.44e-16    3.75e-16     7.60e-16     2.50e-16
    dfb.n0.3.2 dfb.n50.3.2 dfb.n80.3.2 dfb.n110.3.2 dfb.n140.3.2 dfb.n0.2.3
1    -5.14e-15   -3.79e-15   -3.80e-15    -3.74e-15    -3.89e-15  -5.14e-15
2     2.73e-16   -2.10e-15   -1.37e-15    -1.30e-15    -1.25e-15   4.02e-15
3     4.43e-15    5.20e-15    5.98e-15     5.20e-15     5.11e-15   2.34e-15
4    -1.62e-15   -9.34e-16   -1.17e-15    -2.02e-15    -1.25e-15  -1.55e-15
5    -3.54e-15   -4.21e-15   -3.10e-15    -2.89e-15    -3.77e-15  -3.18e-15
6    -5.90e-16   -5.86e-16   -5.95e-16    -5.49e-16    -6.08e-16  -3.03e-16
7     4.13e-16    3.89e-16    3.85e-16     3.49e-16     4.40e-16   4.13e-16
8     4.37e-17    4.52e-17    4.13e-17     4.37e-17     4.83e-17   4.94e-17
9     2.77e-16    2.90e-16    2.91e-16     2.88e-16     2.90e-16   1.36e-16
10   -7.31e-16   -1.49e-16   -3.18e-16    -7.98e-17    -1.64e-16  -2.62e-16
11    2.74e-16    1.71e-16    2.24e-16     1.45e-16     1.81e-16   6.18e-16
12    1.93e-16    2.03e-16    2.09e-16     1.28e-16     1.77e-16   2.26e-16
13   -3.83e-16   -3.10e-16   -2.75e-16    -3.46e-16    -5.30e-16  -2.27e-16
14    1.64e-16    1.77e-16    1.43e-16     2.40e-16     1.45e-16   2.42e-16
15    4.63e-17    3.70e-17    2.51e-17     2.11e-17    -4.74e-18   7.16e-17
16    7.45e-02   -5.21e-17   -1.50e-16    -7.41e-17    -1.01e-16  -7.69e-17
17    1.05e-17    1.06e-18   -8.08e-18    -6.24e-18    -6.13e-18   8.91e-18
18    2.20e-01   -1.75e-17    1.14e-16     1.30e-16     3.83e-17   7.73e-17
19   -2.95e-16   -1.30e-01   -3.56e-16    -3.55e-16    -3.56e-16  -2.14e-16
20   -1.46e-16   -1.28e-16   -9.46e-17    -1.20e-16    -1.39e-16  -8.60e-17
21    1.29e-15   -6.44e-01    1.44e-15     1.56e-15     1.25e-15   1.26e-15
22    3.23e-16    9.85e-16   -5.69e-01     1.05e-15     9.91e-16   6.81e-16
23    1.57e-16    2.76e-16    1.92e-16     1.84e-16     2.40e-16   1.48e-16
24    4.75e-16    3.73e-16    3.90e-01     4.24e-16     3.86e-16   1.23e-16
25   -1.85e-18   -9.96e-19   -5.13e-19     4.70e-03    -1.74e-18  -5.40e-18
26   -4.01e-17   -5.29e-17   -3.65e-17    -2.35e-17    -5.39e-17   1.90e-16
27   -6.38e-17   -3.69e-17   -6.46e-17    -8.89e-02    -5.19e-17  -1.17e-16
28    7.94e-17    7.74e-17    8.61e-17     8.92e-17     4.34e-02   6.42e-17
29    2.92e-16    2.32e-16    2.11e-16     1.88e-16     5.11e-16   4.04e-16
30   -9.85e-17   -9.67e-17   -9.51e-17    -9.62e-17    -1.09e-01  -1.52e-16
31    1.38e-16    2.45e-16    2.50e-16     5.60e-17     2.54e-16  -3.73e-01
32    2.80e-16    3.26e-16    5.45e-16     4.55e-16     4.07e-16   6.29e-01
33    2.96e-16    2.21e-16    3.75e-16     4.71e-16     2.33e-16   2.69e-16
34   -6.16e-16   -5.85e-16   -6.44e-16    -7.19e-16    -6.61e-16  -5.80e-16
35   -1.25e-15   -1.11e-15   -9.67e-16    -1.17e-15    -1.13e-15  -1.23e-15
36   -1.60e-15   -1.43e-15   -1.14e-15    -1.70e-15    -1.75e-15  -1.45e-15
37   -2.28e-16   -2.64e-16   -1.88e-16    -3.25e-16    -8.01e-17  -1.50e-16
38   -4.97e-16   -4.04e-16   -4.18e-16    -3.84e-16    -3.25e-16   6.19e-17
39   -6.22e-16   -4.78e-16   -5.87e-16    -5.93e-16    -6.16e-16  -4.08e-16
40   -6.60e-16   -4.38e-16   -6.95e-16    -4.04e-16    -3.98e-16  -2.74e-19
41    3.89e-17    8.24e-17    1.09e-16     2.94e-17     3.06e-17  -3.46e-16
42   -1.92e-18   -1.32e-18   -1.08e-18    -1.54e-18    -2.16e-18   6.12e-19
43    2.89e-01    2.89e-01    2.89e-01     2.89e-01     2.89e-01   2.89e-01
44   -4.73e-16   -3.66e-16   -4.06e-16    -4.52e-16    -9.76e-17  -3.67e-01
45   -5.82e-01   -5.82e-01   -5.82e-01    -5.82e-01    -5.82e-01   4.56e-16
46   -5.38e-15   -3.70e-15   -4.64e-15    -3.49e-15    -3.77e-15  -5.80e-15
47   -5.55e-17    1.33e-16    8.56e-17     8.60e-17     8.66e-17  -2.68e-16
48    3.17e-15    3.63e-15    4.15e-15     3.51e-15     3.54e-15   1.91e-15
49   -9.62e-16   -6.97e-16   -7.03e-16    -1.21e-15    -7.74e-16  -8.47e-16
50   -5.36e-16   -5.96e-16   -4.47e-16    -4.32e-16    -5.76e-16  -4.82e-16
51   -4.80e-16   -3.93e-16   -4.79e-16    -4.26e-16    -4.57e-16  -2.25e-16
52    8.73e-16    1.02e-15    9.13e-16     8.83e-16     7.39e-16   7.75e-16
53   -1.44e-16   -1.47e-16   -1.18e-16    -1.36e-16    -1.03e-16  -1.28e-16
54   -2.04e-16   -2.11e-16   -2.17e-16    -2.22e-16    -2.12e-16  -1.05e-16
55   -5.13e-17   -9.51e-18   -4.16e-18    -1.70e-17    -1.17e-17  -3.04e-17
56   -3.60e-17   -2.67e-17   -2.31e-17    -2.63e-17    -2.25e-17  -9.87e-17
57    2.03e-16    1.38e-16    1.40e-16     1.25e-16     1.86e-16   2.10e-16
58   -7.68e-17   -1.08e-16   -1.09e-16    -5.81e-17    -8.46e-17  -1.13e-16
59    8.62e-17    7.86e-17    6.01e-17     5.71e-17     5.36e-17   1.04e-16
60    6.93e-17    1.41e-16    1.13e-16     8.00e-17     1.63e-16  -2.93e-17
61   -3.59e-01   -3.32e-16   -2.14e-16    -2.69e-16    -2.47e-16  -2.33e-16
62    1.56e-19    1.63e-17    3.50e-17     4.15e-17     3.34e-17   2.51e-17
63   -5.46e-01   -2.51e-17    4.90e-17     2.33e-17     5.21e-17   2.30e-17
64    8.58e-16   -6.94e-01    8.72e-16     9.40e-16     1.01e-15   8.35e-16
65    1.60e-18    1.09e-18    1.17e-18     1.27e-18     1.39e-18   8.77e-19
66    9.44e-17    9.09e-02    8.30e-17     9.80e-17     6.72e-17   4.20e-17
67   -1.10e-16   -1.52e-16   -1.68e-01    -1.63e-16    -1.33e-16  -3.86e-17
68    3.03e-17    2.81e-17    4.21e-17     3.62e-17     4.54e-17   3.84e-17
69   -1.13e-16   -5.63e-17   -2.84e-01    -1.07e-18     3.64e-18   2.68e-17
70    6.66e-17   -7.77e-17   -7.96e-17    -3.13e-01    -2.64e-17  -1.13e-16
71   -5.05e-17   -8.82e-17   -1.13e-16    -6.42e-17    -7.48e-17   4.86e-17
72    5.19e-18    2.64e-18   -2.54e-17     1.08e-01    -1.27e-17  -7.47e-17
73    1.38e-16    1.97e-16    1.53e-16     1.55e-16    -1.75e-01   1.23e-16
74    1.37e-18   -6.01e-18   -7.27e-18    -7.62e-18    -1.97e-17  -2.09e-17
75   -1.57e-17   -1.78e-17   -1.20e-17    -4.57e-18     4.15e-02  -2.39e-17
76   -9.92e-17   -7.84e-17   -1.31e-16    -1.50e-16    -1.04e-16  -1.29e-01
77    2.88e-17    7.89e-17    1.17e-16     6.65e-17     8.37e-17  -3.47e-01
78    1.89e-16    2.71e-16    2.47e-16     3.60e-17     2.16e-16   8.40e-17
79   -8.87e-17   -9.70e-17   -5.97e-17    -9.85e-17    -1.00e-16  -1.17e-16
80   -2.87e-16   -2.36e-16   -2.99e-16    -3.20e-16    -3.08e-16  -6.14e-17
81   -1.90e-15   -1.48e-15   -1.57e-15    -1.71e-15    -1.58e-15  -1.69e-15
82   -2.14e-16   -2.09e-16   -1.73e-16    -1.35e-16    -1.71e-16  -2.30e-16
83   -1.22e-16   -1.06e-16   -1.01e-16    -1.06e-16    -7.96e-17   6.75e-17
84   -5.46e-16   -4.41e-16   -5.29e-16    -5.29e-16    -5.00e-16  -2.96e-16
85   -4.60e-17   -3.97e-17   -5.21e-17    -4.89e-17    -3.71e-17  -1.50e-17
86   -3.00e-17   -6.92e-18    1.12e-17    -1.42e-17    -5.57e-18  -1.41e-16
87   -8.77e-18    1.14e-18    1.00e-17     9.14e-18    -1.12e-17   3.12e-17
88    6.44e-02    6.44e-02    6.44e-02     6.44e-02     6.44e-02   6.44e-02
89   -1.86e-17   -3.27e-17   -5.11e-18     9.16e-18    -7.14e-17   1.21e-01
90   -1.69e-01   -1.69e-01   -1.69e-01    -1.69e-01    -1.69e-01  -5.36e-17
91    2.08e-15    1.37e-15    1.81e-15     1.36e-15     1.41e-15   2.28e-15
92    1.28e-16   -1.33e-15   -9.06e-16    -1.00e-15    -9.12e-16   2.48e-15
93   -5.69e-16   -6.59e-16   -7.56e-16    -6.22e-16    -6.19e-16  -2.46e-16
94    1.93e-16    1.41e-16    1.29e-16     2.38e-16     1.64e-16   2.10e-16
95   -1.11e-15   -1.31e-15   -9.44e-16    -9.13e-16    -1.17e-15  -1.05e-15
96    1.27e-16    1.08e-16    1.25e-16     1.11e-16     1.13e-16   4.22e-17
97   -4.32e-16   -4.59e-16   -3.78e-16    -3.82e-16    -2.59e-16  -3.70e-16
98    1.84e-16    1.89e-16    1.77e-16     1.79e-16     1.18e-16   2.15e-16
99    2.88e-16    2.82e-16    2.99e-16     2.79e-16     2.96e-16   1.37e-16
100  -4.36e-16   -7.90e-17   -1.24e-17    -1.47e-16    -9.59e-17  -1.28e-16
101   1.35e-16    1.21e-16    1.25e-16     1.22e-16     1.21e-16   5.00e-16
102  -1.32e-17   -9.91e-18   -1.35e-17    -1.08e-17    -2.43e-17  -3.96e-17
103   2.51e-17   -3.31e-17   -5.08e-17    -3.90e-17    -3.98e-17  -2.96e-17
104   9.52e-18    8.88e-18    7.82e-18     6.73e-18     9.40e-18   5.17e-18
105   2.89e-16    2.22e-16    2.55e-16     2.96e-16     2.51e-16   2.30e-16
106   2.83e-01    1.92e-16    1.22e-16     1.75e-16     2.04e-16   1.98e-16
107   6.21e-17    3.58e-17    9.95e-18     1.54e-17     5.26e-18   4.21e-17
108   3.21e-01   -7.25e-17   -9.72e-17    -8.99e-17    -5.69e-17   2.68e-17
109  -9.71e-16    8.34e-01   -9.08e-16    -1.01e-15    -1.06e-15  -7.85e-16
110  -5.02e-17   -2.20e-17   -5.84e-17    -6.54e-17    -8.12e-17  -3.42e-17
111   6.98e-16    5.48e-01    7.95e-16     8.59e-16     6.30e-16   6.23e-16
112   6.53e-16    7.00e-16    7.47e-01     8.35e-16     6.92e-16   3.95e-16
113   1.64e-17    4.61e-17    3.63e-17     3.93e-17     5.64e-17   2.62e-17
114   9.18e-17    8.14e-17   -1.05e-01     9.27e-17     8.38e-17   6.18e-17
115   1.10e-16    2.12e-16    1.85e-16     3.08e-01     1.71e-16   2.65e-16
116   2.15e-19   -2.63e-19    1.81e-19    -4.04e-18    -1.82e-18  -1.21e-17
117   1.05e-17    7.85e-18    1.40e-17    -1.88e-02     5.71e-18   9.07e-18
118  -1.58e-16   -1.59e-16   -1.46e-16    -1.36e-16     1.32e-01  -1.11e-16
119   2.14e-16    1.73e-16    1.78e-16     2.53e-16     3.20e-16   3.13e-16
120  -4.10e-17   -3.79e-17   -3.45e-17    -3.48e-17     6.76e-02  -5.24e-17
121   7.79e-17   -5.05e-17    2.67e-16     2.41e-16     1.08e-16   5.05e-01
122  -9.71e-17   -1.19e-17   -1.42e-17    -2.23e-17    -1.07e-17  -2.74e-01
123  -3.07e-16   -2.88e-16   -3.49e-16    -1.34e-16    -4.25e-16  -5.71e-16
124  -1.33e-16   -1.45e-16   -7.45e-17    -1.86e-16    -1.61e-16  -2.36e-16
125  -2.76e-16   -1.76e-16   -2.25e-16    -2.69e-16    -2.49e-16  -2.38e-16
126   4.65e-16    3.75e-16    4.07e-16     5.08e-16     4.08e-16   3.42e-16
127  -1.44e-16   -7.72e-17   -3.29e-17     4.36e-17    -8.18e-17  -2.56e-16
128  -1.00e-16   -7.45e-17   -7.09e-17    -6.65e-17    -5.96e-17   7.00e-17
129   4.66e-17    4.73e-17    4.92e-17     5.74e-17     5.66e-17   6.33e-17
130  -2.35e-16   -1.66e-16   -2.55e-16    -2.47e-16    -1.19e-16  -1.42e-16
131  -4.45e-19    2.88e-18    2.17e-17     8.83e-18    -2.82e-18   2.99e-17
132   6.64e-17    4.86e-17    4.65e-17     7.18e-17     6.90e-17  -8.19e-18
133  -3.55e-01   -3.55e-01   -3.55e-01    -3.55e-01    -3.55e-01  -3.55e-01
134   3.73e-17    4.28e-17    7.66e-17     1.10e-16    -8.56e-17   2.45e-01
135   7.61e-01    7.61e-01    7.61e-01     7.61e-01     7.61e-01   5.70e-16
    dfb.n50.2.3 dfb.n80.2.3 dfb.n110.2.3 dfb.n0.3.3 dfb.n50.3.3 dfb.n80.3.3
1     -3.92e-15   -4.03e-15    -3.59e-15  -5.14e-15   -3.89e-15   -3.92e-15
2      2.64e-15    2.77e-15     2.64e-15   1.26e-16   -1.35e-15   -1.21e-15
3      2.71e-15    3.07e-15     2.70e-15   4.59e-15    5.09e-15    5.34e-15
4     -1.31e-15   -1.50e-15    -2.08e-15  -1.24e-15   -1.02e-15   -1.18e-15
5     -1.96e-15   -2.06e-15    -1.80e-15  -4.32e-15   -2.99e-15   -3.15e-15
6     -2.91e-16   -2.76e-16    -2.16e-16  -6.50e-16   -6.57e-16   -6.12e-16
7      3.09e-16    3.53e-16     3.15e-16   4.90e-16    4.04e-16    4.19e-16
8      4.86e-17    5.23e-17     4.80e-17   4.24e-17    4.07e-17    4.72e-17
9      1.37e-16    1.37e-16     1.47e-16   2.88e-16    2.87e-16    2.92e-16
10     5.67e-17   -8.06e-17    -1.08e-16  -2.74e-16    1.16e-17   -1.43e-16
11     4.12e-16    3.69e-16     3.75e-16   3.42e-16    1.55e-16    1.40e-16
12     2.81e-16    1.93e-16     2.18e-16   1.76e-16    2.35e-16    1.31e-16
13    -3.74e-16   -5.84e-16    -2.91e-16  -3.67e-16   -3.04e-16   -6.52e-16
14     1.71e-16    1.46e-16     1.45e-16   1.79e-16    1.87e-16    1.23e-16
15     7.85e-17    8.70e-17     7.48e-17   3.69e-17    3.24e-17    5.97e-17
16    -9.45e-17   -1.12e-16    -1.12e-16  -6.97e-17   -9.86e-17   -7.65e-17
17     2.30e-18    5.35e-18    -4.96e-18   4.93e-18   -4.21e-19   -7.97e-18
18     6.75e-17    1.14e-16     1.56e-17  -1.50e-17    1.24e-17    6.66e-17
19    -1.66e-16   -1.86e-16    -1.92e-16  -3.82e-16   -3.15e-16   -3.08e-16
20    -1.08e-16   -9.82e-17    -1.10e-16  -1.05e-16   -1.40e-16   -1.39e-16
21     1.06e-15    1.18e-15     1.31e-15   1.36e-15    1.21e-15    1.16e-15
22     7.31e-16    7.58e-16     8.02e-16   6.64e-16    7.58e-16    8.32e-16
23     1.57e-16    2.34e-16     1.85e-16   1.68e-16    1.91e-16    2.11e-16
24     7.37e-17    2.27e-16     2.23e-16   4.20e-16    2.20e-16    4.69e-16
25    -4.62e-18   -3.03e-18    -4.18e-18  -2.26e-18   -1.32e-18    3.23e-19
26     1.94e-17    9.86e-18    -1.78e-16   7.05e-17   -7.51e-17   -6.54e-17
27    -7.09e-17   -7.73e-17    -8.21e-17  -5.37e-17   -3.09e-17   -5.00e-17
28     7.47e-17    6.90e-17     7.62e-17   8.61e-17    9.46e-17    8.62e-17
29     3.69e-16    3.71e-16     3.51e-16   2.58e-16    2.05e-16    3.24e-16
30    -1.42e-16   -1.32e-16    -1.57e-16  -1.00e-16   -1.04e-16   -8.56e-17
31     5.68e-16    5.13e-16     5.30e-16  -3.73e-01    1.75e-16    1.46e-16
32     2.72e-16    3.07e-16     2.34e-16   2.35e-16    3.87e-16    4.35e-16
33     3.26e-16    5.13e-16     4.31e-16   3.68e-01    2.62e-16    4.87e-16
34    -3.33e-01   -4.60e-16    -5.31e-16  -7.71e-16   -3.33e-01   -4.90e-16
35     6.22e-01   -7.71e-16    -9.40e-16  -1.29e-15   -6.56e-16   -1.15e-15
36    -9.68e-16   -1.17e-15    -1.25e-15  -1.81e-15    7.95e-01   -1.60e-15
37    -4.18e-16    6.83e-01    -4.41e-16  -2.83e-16   -5.10e-16    6.83e-01
38     6.34e-17   -2.33e-01     4.88e-17  -3.53e-16   -3.82e-16   -3.42e-16
39    -5.51e-16   -6.29e-16    -4.01e-16  -5.45e-16   -5.88e-16   -2.83e-01
40     4.20e-17    5.22e-17    -3.62e-01  -3.40e-16   -4.72e-16   -3.92e-16
41    -3.76e-16   -3.57e-16     2.91e-01   7.64e-17    1.18e-16    4.91e-17
42    -3.07e-19    1.65e-19    -7.96e-19  -6.83e-19   -1.04e-18   -5.97e-19
43     2.89e-01    2.89e-01     2.89e-01   2.89e-01    2.89e-01    2.89e-01
44    -3.67e-01   -3.67e-01    -3.67e-01  -3.89e-16   -4.29e-16   -3.31e-16
45     4.62e-16    5.53e-16     9.61e-16  -5.82e-01   -5.82e-01   -5.82e-01
46    -4.55e-15   -4.47e-15    -4.35e-15  -5.63e-15   -4.14e-15   -4.16e-15
47    -1.76e-16   -1.78e-16    -1.73e-16  -3.03e-17    7.57e-17    7.04e-17
48     1.98e-15    2.39e-15     2.13e-15   3.48e-15    3.50e-15    3.79e-15
49    -6.15e-16   -6.82e-16    -9.69e-16  -8.18e-16   -5.60e-16   -7.19e-16
50    -2.39e-16   -2.80e-16    -2.14e-16  -6.66e-16   -4.49e-16   -4.49e-16
51    -1.75e-16   -2.19e-16    -1.07e-16  -5.00e-16   -4.79e-16   -4.74e-16
52     7.29e-16    6.66e-16     6.79e-16   1.04e-15    9.46e-16    9.36e-16
53    -1.39e-16   -1.62e-16    -1.46e-16  -1.19e-16   -1.25e-16   -1.64e-16
54    -1.11e-16   -1.16e-16    -1.20e-16  -2.14e-16   -2.12e-16   -2.26e-16
55    -2.01e-17   -1.95e-17    -2.12e-17  -1.34e-17   -1.19e-17   -1.17e-17
56    -5.32e-17   -4.57e-17    -4.73e-17  -7.20e-17   -2.51e-17   -1.76e-17
57     1.88e-16    1.71e-16     2.04e-16   2.49e-16    1.58e-16    1.46e-16
58    -3.35e-17   -8.79e-17    -4.19e-17  -1.39e-16   -1.04e-16   -1.56e-16
59     1.22e-16    1.05e-16     1.24e-16   1.10e-16    8.64e-17    4.49e-17
60     4.69e-17   -2.46e-17     7.07e-18   1.02e-16    1.61e-16    8.09e-17
61    -2.19e-16   -1.86e-16    -2.35e-16  -2.17e-16   -3.14e-16   -3.22e-16
62     2.60e-17    3.40e-17     2.00e-17   1.69e-17    1.86e-17    2.45e-17
63     1.80e-17    9.38e-17     1.77e-16  -1.26e-16   -5.44e-17   -1.10e-16
64     6.49e-16    6.49e-16     6.31e-16   1.03e-15    8.09e-16    7.81e-16
65     1.41e-18    1.45e-18     1.02e-18   1.02e-18    1.59e-18    1.53e-18
66     3.88e-17    3.37e-17     5.30e-17   7.96e-17    6.56e-17    6.53e-17
67    -5.32e-17   -5.38e-17    -4.65e-17  -1.30e-16   -1.39e-16   -9.66e-17
68     4.35e-17    3.84e-17     4.85e-17   3.52e-17    3.40e-17    2.39e-17
69     2.02e-17    8.46e-17     1.55e-16  -8.24e-17   -1.02e-16   -9.62e-18
70    -7.54e-17   -3.64e-17    -9.99e-17  -3.88e-19    4.98e-17    7.46e-17
71    -3.24e-17   -3.61e-17    -1.47e-16  -1.03e-17   -8.17e-17   -9.39e-17
72    -6.03e-17   -5.98e-17    -4.76e-17  -2.35e-17   -1.06e-17   -2.23e-17
73     1.33e-16    1.29e-16     1.33e-16   1.45e-16    1.66e-16    1.67e-16
74    -1.82e-17   -2.90e-17    -1.81e-17  -8.49e-18   -3.32e-18   -1.13e-17
75    -2.14e-17   -2.55e-17    -2.58e-17  -1.24e-17   -1.30e-17   -1.33e-17
76    -5.30e-17   -8.04e-17    -7.22e-17  -1.29e-01   -7.25e-17   -8.36e-17
77     2.28e-17    7.63e-17    -8.09e-19   7.32e-17    1.35e-16    1.13e-16
78     3.86e-16    4.69e-16     4.99e-16  -9.66e-01    1.82e-16    3.48e-16
79     1.08e-01   -4.90e-17    -3.19e-17  -1.19e-16    1.08e-01   -9.14e-17
80    -3.73e-01   -2.63e-17    -6.92e-17  -3.46e-16   -9.34e-17   -2.37e-16
81    -1.55e-15   -1.26e-15    -1.23e-15  -2.01e-15   -1.32e+00   -1.62e-15
82    -2.26e-16   -2.77e-01    -1.61e-16  -1.33e-16   -1.52e-16   -2.77e-01
83     6.92e-17    1.27e-01     2.11e-17  -8.23e-17   -9.20e-17   -9.18e-17
84    -4.35e-16   -4.71e-16    -2.97e-16  -5.28e-16   -5.85e-16    3.72e-01
85    -2.66e-17   -2.30e-17     3.98e-02  -2.75e-17   -3.72e-17   -3.65e-17
86    -1.73e-16   -1.55e-16    -1.79e-01   1.29e-18   -3.54e-19   -2.55e-18
87     2.90e-17    2.12e-17     3.71e-17   2.97e-17    4.52e-18   -7.41e-18
88     6.44e-02    6.44e-02     6.44e-02   6.44e-02    6.44e-02    6.44e-02
89     1.21e-01    1.21e-01     1.21e-01  -5.14e-17   -2.90e-17   -3.20e-17
90    -3.92e-17   -3.98e-18     9.63e-17  -1.69e-01   -1.69e-01   -1.69e-01
91     1.83e-15    1.75e-15     1.75e-15   2.02e-15    1.54e-15    1.51e-15
92     1.60e-15    1.79e-15     1.67e-15  -1.36e-16   -1.10e-15   -8.30e-16
93    -3.35e-16   -3.40e-16    -3.14e-16  -5.67e-16   -6.77e-16   -6.67e-16
94     2.12e-16    2.07e-16     2.76e-16   1.46e-16    1.41e-16    1.42e-16
95    -6.94e-16   -7.40e-16    -6.47e-16  -1.32e-15   -9.41e-16   -1.08e-15
96     4.64e-17    4.37e-17     5.68e-17   1.15e-16    1.21e-16    1.10e-16
97    -2.18e-16   -3.40e-16    -2.74e-16  -4.95e-16   -3.34e-16   -4.18e-16
98     1.99e-16    2.03e-16     2.04e-16   1.88e-16    1.76e-16    1.84e-16
99     1.36e-16    1.28e-16     1.36e-16   2.99e-16    2.86e-16    2.88e-16
100   -5.00e-18   -3.03e-17     8.18e-19  -1.52e-16   -7.15e-17   -9.50e-17
101    2.98e-16    2.71e-16     2.72e-16   2.58e-16    8.70e-17    8.06e-17
102   -2.07e-17   -2.35e-17    -2.48e-17  -2.75e-17   -1.17e-18   -9.27e-18
103    6.44e-17   -2.60e-17     1.07e-17  -5.63e-17   -9.39e-17   -2.36e-16
104    5.19e-18    3.86e-18     2.91e-18   1.14e-17    9.60e-18    7.00e-18
105    1.24e-16    1.38e-16     1.93e-16   2.79e-16    2.09e-16    2.34e-16
106    1.92e-16    1.80e-16     1.67e-16   1.30e-16    2.17e-16    2.51e-16
107    2.56e-17    1.05e-17     3.10e-17   4.91e-17    3.91e-17    1.84e-17
108   -3.53e-17   -4.59e-17    -5.08e-17   2.11e-17   -3.11e-17   -3.69e-17
109   -5.71e-16   -5.32e-16    -6.33e-16  -1.09e-15   -8.68e-16   -7.86e-16
110   -3.81e-17   -5.18e-17    -5.70e-17  -5.15e-17   -7.52e-17   -6.72e-17
111    5.19e-16    5.48e-16     7.23e-16   8.22e-16    6.89e-16    6.91e-16
112    3.91e-16    5.48e-16     3.14e-16   7.91e-16    7.24e-16    8.11e-16
113    4.01e-17    6.10e-17     3.81e-17   3.57e-17    4.32e-17    6.26e-17
114    5.86e-17    7.97e-17     9.42e-17   6.81e-17    5.61e-17    9.75e-17
115    2.13e-16    1.31e-16     2.18e-16   1.63e-16    1.12e-16    3.99e-17
116   -6.18e-18   -5.41e-18     2.25e-18  -6.29e-18   -4.75e-19    1.64e-19
117    8.35e-18    8.45e-18     9.01e-18   7.07e-18    8.61e-18    8.74e-18
118   -1.11e-16   -1.04e-16    -1.05e-16  -1.54e-16   -1.64e-16   -1.70e-16
119    2.93e-16    3.51e-16     3.29e-16   1.61e-16    1.66e-16    1.91e-16
120   -5.09e-17   -5.72e-17    -5.57e-17  -3.18e-17   -3.61e-17   -2.95e-17
121    1.83e-16    2.73e-16     1.78e-16   5.05e-01    3.26e-17    9.89e-17
122    2.48e-17    2.14e-17     7.70e-18  -2.02e-17   -1.47e-17   -2.08e-17
123   -4.67e-16   -4.83e-16    -4.32e-16   5.70e-01   -2.92e-16   -4.17e-16
124    2.24e-01   -1.49e-16    -1.54e-16  -1.36e-16    2.24e-01   -1.87e-16
125   -2.41e-01   -2.46e-16    -3.01e-16  -2.68e-16   -1.48e-16   -2.38e-16
126    5.86e-16    3.31e-16     3.99e-16   4.18e-16    4.58e-01    3.93e-16
127   -2.42e-16   -3.96e-01    -1.44e-16  -4.57e-17   -6.22e-17   -3.96e-01
128    5.75e-17    1.06e-01     1.78e-17  -6.54e-17   -7.37e-17   -5.39e-17
129    9.25e-17    4.27e-17     5.99e-17   6.52e-17    8.66e-17   -8.82e-02
130   -1.71e-16   -1.86e-16     3.22e-01  -1.28e-16   -1.33e-16   -1.34e-16
131    2.09e-17    4.00e-17    -1.11e-01   1.66e-17    7.64e-18    8.11e-18
132   -1.47e-17   -9.60e-18    -7.21e-18   4.35e-17    5.76e-17    5.05e-17
133   -3.55e-01   -3.55e-01    -3.55e-01  -3.55e-01   -3.55e-01   -3.55e-01
134    2.45e-01    2.45e-01     2.45e-01  -6.58e-18    2.64e-17    6.11e-18
135    6.10e-16    3.18e-16    -5.28e-17   7.61e-01    7.61e-01    7.61e-01
    dfb.n110.3.3    dffit   cov.r   cook.d   hat inf
1      -3.42e-15 -1.16470 0.86785 2.44e-02 0.407   *
2      -1.35e-15 -1.26808 0.67728 2.88e-02 0.407    
3       5.04e-15 -0.87162 1.57000 1.38e-02 0.407    
4      -1.83e-15 -0.81767 1.71972 1.22e-02 0.407    
5      -2.97e-15 -1.79044 0.14385 5.57e-02 0.407    
6      -5.43e-16 -0.34636 2.98539 2.20e-03 0.407    
7       4.26e-16  0.27434 3.12339 1.38e-03 0.407   *
8       4.32e-17 -0.03107 3.36727 1.78e-05 0.407   *
9       3.03e-16 -0.07968 3.34897 1.17e-04 0.407   *
10     -1.95e-16 -0.67221 2.13698 8.25e-03 0.407    
11      1.34e-16 -0.56815 2.43310 5.91e-03 0.407    
12      1.52e-16  0.47717 2.67779 4.17e-03 0.407    
13     -1.43e-16 -1.85474 0.11502 5.96e-02 0.407   *
14      1.30e-16  0.61118 2.31197 6.83e-03 0.407    
15      4.56e-17 -0.37235 2.92958 2.55e-03 0.407    
16     -1.10e-16 -0.16478 3.27917 5.00e-04 0.407   *
17     -1.06e-17 -0.05133 3.36159 4.85e-05 0.407   *
18     -3.61e-17  0.48699 2.65235 4.35e-03 0.407    
19     -3.37e-16  0.28662 3.10172 1.51e-03 0.407   *
20     -1.37e-16  0.21803 3.21222 8.74e-04 0.407   *
21      1.45e-15 -1.42333 0.44973 3.60e-02 0.407    
22      8.89e-16  1.25790 0.69465 2.83e-02 0.407    
23      2.46e-16  0.35767 2.96148 2.35e-03 0.407    
24      4.72e-16  0.86326 1.59290 1.35e-02 0.407    
25     -7.84e-19 -0.01039 3.37020 1.99e-06 0.407   *
26     -2.65e-16 -0.47653 2.67944 4.16e-03 0.407    
27     -5.28e-17 -0.19652 3.24134 7.11e-04 0.407   *
28      9.74e-17 -0.09594 3.33930 1.69e-04 0.407   *
29      1.98e-16 -0.81797 1.71889 1.22e-02 0.407    
30     -1.20e-16 -0.24135 3.17760 1.07e-03 0.407   *
31      2.86e-16  0.82554 1.69763 1.24e-02 0.407    
32      4.02e-16  1.39067 0.49199 3.44e-02 0.407    
33      4.00e-16  0.81383 1.73055 1.20e-02 0.407    
34     -5.18e-16  0.73531 1.95475 9.86e-03 0.407    
35     -1.28e-15  1.37428 0.51429 3.36e-02 0.407    
36     -1.71e-15  1.75688 0.16121 5.38e-02 0.407    
37     -4.52e-16 -1.51111 0.34994 4.03e-02 0.407    
38     -3.26e-16 -0.51576 2.57633 4.87e-03 0.407    
39     -4.85e-16 -0.62544 2.27134 7.15e-03 0.407    
40     -3.62e-01  0.80070 1.76763 1.17e-02 0.407    
41     -5.92e-17  0.64324 2.22038 7.56e-03 0.407    
42      2.39e-03  0.00528 3.37047 5.14e-07 0.407   *
43      2.89e-01  0.63971 2.23049 7.48e-03 0.407    
44     -4.50e-16  0.81205 1.73555 1.20e-02 0.407    
45     -5.82e-01  1.28623 0.64710 2.96e-02 0.407    
46     -4.14e-15  2.29486 0.02075 8.84e-02 0.407   *
47      7.70e-17 -0.18327 3.25789 6.18e-04 0.407   *
48      3.66e-15  1.12798 0.94317 2.29e-02 0.407    
49     -1.06e-15  1.00661 1.21951 1.83e-02 0.407    
50     -4.52e-16  0.58157 2.39561 6.19e-03 0.407    
51     -3.16e-16  0.48833 2.64884 4.37e-03 0.407    
52      1.01e-15 -0.95623 1.34560 1.66e-02 0.407    
53     -1.40e-16 -0.21094 3.22213 8.19e-04 0.407   *
54     -2.41e-16 -0.10425 3.33368 2.00e-04 0.407   *
55     -5.96e-18  0.08804 3.34422 1.43e-04 0.407   *
56     -2.25e-17 -0.16339 3.28069 4.91e-04 0.407   *
57      1.65e-16 -0.69321 2.07634 8.77e-03 0.407    
58     -7.71e-17  0.58216 2.39397 6.20e-03 0.407    
59      9.08e-17 -0.55690 2.46430 5.68e-03 0.407    
60      1.10e-16 -0.64664 2.21060 7.64e-03 0.407    
61     -2.49e-16  0.79344 1.78825 1.15e-02 0.407    
62      3.05e-17 -0.18902 3.25083 6.57e-04 0.407   *
63      3.42e-17 -1.20724 0.78558 2.61e-02 0.407    
64      8.18e-16  1.53442 0.32663 4.15e-02 0.407    
65      1.13e-18  0.00383 3.37052 2.70e-07 0.407   *
66      8.75e-17  0.20094 3.23558 7.43e-04 0.407   *
67     -1.38e-16  0.37235 2.92958 2.55e-03 0.407    
68      3.30e-17 -0.19262 3.24631 6.83e-04 0.407   *
69      1.32e-16 -0.62756 2.26530 7.20e-03 0.407    
70     -2.89e-17  0.69209 2.07957 8.74e-03 0.407    
71     -1.74e-16  0.51997 2.56503 4.95e-03 0.407    
72      1.26e-17  0.23815 3.18253 1.04e-03 0.407   *
73      1.55e-16  0.38804 2.89451 2.76e-03 0.407    
74      5.89e-18 -0.11005 3.32948 2.23e-04 0.407   *
75     -9.47e-18  0.09170 3.34199 1.55e-04 0.407   *
76     -7.02e-17  0.28475 3.10505 1.49e-03 0.407   *
77      1.28e-16 -0.76799 1.86085 1.07e-02 0.407    
78      3.59e-16 -2.13663 0.03980 7.75e-02 0.407    
79     -7.28e-17 -0.23827 3.18235 1.04e-03 0.407   *
80     -3.15e-16 -0.82495 1.69929 1.24e-02 0.407    
81     -1.50e-15 -2.91829 0.00112 1.36e-01 0.407   *
82     -1.59e-16  0.61230 2.30880 6.86e-03 0.407    
83     -9.48e-17  0.28115 3.11147 1.45e-03 0.407   *
84     -4.75e-16  0.82329 1.70393 1.23e-02 0.407    
85      3.98e-02 -0.08810 3.34418 1.43e-04 0.407   *
86     -1.35e-17 -0.39597 2.87639 2.88e-03 0.407    
87     -8.90e-02 -0.19687 3.24089 7.13e-04 0.407   *
88      6.44e-02  0.14241 3.30206 3.73e-04 0.407   *
89     -1.82e-17 -0.26648 3.13684 1.31e-03 0.407   *
90     -1.69e-01  0.37439 2.92507 2.57e-03 0.407    
91      1.55e-15 -1.05120 1.11327 1.99e-02 0.407    
92     -9.71e-16  1.46081 0.40474 3.78e-02 0.407    
93     -6.42e-16 -0.24955 3.16468 1.15e-03 0.407   *
94      2.21e-16 -0.18472 3.25613 6.28e-04 0.407   *
95     -8.81e-16  1.17470 0.84801 2.48e-02 0.407    
96      1.32e-16 -0.14131 3.30311 3.68e-04 0.407   *
97     -3.93e-16  0.67697 2.12323 8.37e-03 0.407    
98      1.77e-16  0.24205 3.17651 1.08e-03 0.407   *
99      2.92e-16  0.18396 3.25705 6.23e-04 0.407   *
100    -5.88e-17  0.58321 2.39101 6.22e-03 0.407    
101     4.08e-17  0.73343 1.96019 9.81e-03 0.407    
102    -1.75e-17  0.21408 3.21778 8.43e-04 0.407   *
103    -1.05e-16  1.23530 0.73426 2.73e-02 0.407    
104     8.42e-18 -0.05377 3.36071 5.32e-05 0.407   *
105     2.86e-16  1.02584 1.17304 1.90e-02 0.407    
106     1.81e-16 -0.62638 2.26865 7.17e-03 0.407    
107     1.87e-17  0.24042 3.17904 1.06e-03 0.407   *
108    -4.88e-17  0.70869 2.03161 9.16e-03 0.407    
109    -9.51e-16 -1.84373 0.11957 5.89e-02 0.407    
110    -7.89e-17 -0.22187 3.20674 9.06e-04 0.407   *
111     8.73e-16  1.21274 0.77534 2.64e-02 0.407    
112     6.24e-16 -1.65183 0.22745 4.78e-02 0.407    
113     3.84e-17 -0.16473 3.27923 4.99e-04 0.407   *
114     1.29e-16 -0.23222 3.19153 9.92e-04 0.407   *
115     1.87e-16 -0.68156 2.10999 8.48e-03 0.407    
116     8.13e-18 -0.04315 3.36422 3.43e-05 0.407   *
117     9.11e-18 -0.04158 3.36467 3.18e-05 0.407   *
118    -1.43e-16 -0.29180 3.09233 1.57e-03 0.407   *
119     1.51e-16  0.93034 1.41269 1.57e-02 0.407    
120    -2.46e-17  0.14956 3.29509 4.12e-04 0.407   *
121    -3.15e-17 -1.11758 0.96522 2.25e-02 0.407    
122     2.72e-18 -0.60473 2.33029 6.69e-03 0.407    
123    -3.83e-16  1.26129 0.68883 2.85e-02 0.407    
124    -1.81e-16 -0.49464 2.63232 4.48e-03 0.407    
125    -3.04e-16 -0.53255 2.53104 5.19e-03 0.407    
126     4.17e-16  1.01377 1.20209 1.86e-02 0.407    
127    -9.84e-18  0.87625 1.55737 1.39e-02 0.407    
128    -7.17e-17  0.23367 3.18934 1.00e-03 0.407   *
129     4.84e-17 -0.19507 3.24321 7.00e-04 0.407   *
130     3.22e-01 -0.71122 2.02429 9.23e-03 0.407    
131    -3.50e-17 -0.24554 3.17105 1.11e-03 0.407   *
132     8.66e-02  0.19158 3.24763 6.75e-04 0.407   *
133    -3.55e-01 -0.78410 1.81481 1.12e-02 0.407    
134     6.11e-17 -0.54232 2.50439 5.39e-03 0.407    
135     7.61e-01 -1.68325 0.20561 4.96e-02 0.407   *
influenceIndexPlot(modelo.dbca)

Cumplimiento de supuestos del modelo lineal general


Independencia de residuos

\(H_0: \text{Los residuos del rendimiento son completamente aleatorios e independientes}\)

\(H_1: \text{Los residuos del rendimiento no son completamente aleatorios e independientes}\)

durbinWatsonTest(modelo.dbca,
                 reps = 5000,
                 max.lag = 5)
 lag Autocorrelation D-W Statistic p-value
   1      0.10271535      1.750748  0.0524
   2      0.09963745      1.736672  0.1480
   3      0.24118676      1.438765  0.0168
   4      0.04357747      1.826377  0.6000
   5      0.03955075      1.800747  0.5564
 Alternative hypothesis: rho[lag] != 0
dwtest(modelo.dbca, alternative = "two.sided")

    Durbin-Watson test

data:  modelo.dbca
DW = 1.7507, p-value = 0.4711
alternative hypothesis: true autocorrelation is not 0

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los residuos del rendimiento son completamente aleatorios e independientes.

Normalidad de residuos

\(H_0: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

\(H_1: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

shapiro.test(rstudent(modelo.dbca))

    Shapiro-Wilk normality test

data:  rstudent(modelo.dbca)
W = 0.98693, p-value = 0.2291
ad.test(rstudent(modelo.dbca))

    Anderson-Darling normality test

data:  rstudent(modelo.dbca)
A = 0.50255, p-value = 0.2024
lillie.test(rstudent(modelo.dbca))

    Lilliefors (Kolmogorov-Smirnov) normality test

data:  rstudent(modelo.dbca)
D = 0.073687, p-value = 0.06947
ks.test(rstudent(modelo.dbca), "pnorm",
        alternative = "two.sided")

    Asymptotic one-sample Kolmogorov-Smirnov test

data:  rstudent(modelo.dbca)
D = 0.070607, p-value = 0.5114
alternative hypothesis: two-sided
cvm.test(rstudent(modelo.dbca))

    Cramer-von Mises normality test

data:  rstudent(modelo.dbca)
W = 0.078414, p-value = 0.2154
pearson.test(rstudent(modelo.dbca))

    Pearson chi-square normality test

data:  rstudent(modelo.dbca)
P = 15.111, p-value = 0.2354
sf.test(rstudent(modelo.dbca))

    Shapiro-Francia normality test

data:  rstudent(modelo.dbca)
W = 0.9844, p-value = 0.1135

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la distribución de los residuos del rendimiento es similar a la función normal o gaussiana.

Homocedasticidad

\(H_0\): La varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento

\(H_1\): La varianza del rendimiento no es constante con respecto a los valores ajustados del rendimiento

ncvTest(modelo.dbca)
Non-constant Variance Score Test 
Variance formula: ~ fitted.values 
Chisquare = 3.795665, Df = 1, p = 0.051385
bptest(modelo.dbca)

    studentized Breusch-Pagan test

data:  modelo.dbca
BP = 77.15, df = 54, p-value = 0.02102
bptest(modelo.dbca, studentize = F)

    Breusch-Pagan test

data:  modelo.dbca
BP = 92.635, df = 54, p-value = 0.000839
olsrr::ols_test_breusch_pagan(modelo.dbca)

 Breusch Pagan Test for Heteroskedasticity
 -----------------------------------------
 Ho: the variance is constant            
 Ha: the variance is not constant        

              Data               
 --------------------------------
 Response : rdto 
 Variables: fitted values of rdto 

        Test Summary          
 -----------------------------
 DF            =    1 
 Chi2          =    3.795665 
 Prob > Chi2   =    0.05138547 

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento.

Recomendación. Debido a que se cumple con el supuesto de homocedasticidad, para evaluar los efectos de los tratamientos con respecto al rendimiento, se debe proceder a realizar el análisis de varianza.

Estadísticas globales

# modelo.dbca %>% gvlma()

Análisis de varianza

\[Y_{ijkl} = \mu + \tau_{i} + \delta_{l} + \text{Error}(\tau\delta)_{il} + \beta_{j} + \text{Error}(\tau\beta\delta)_{ijl} + \gamma_{k} + (\tau\gamma)_{ik} + \epsilon_{ijkl}\]

\[\hat{Y}_{ijkl} = \mu + \tau_{i} + \delta_{l} + \text{Error}(\tau\delta)_{il} + \beta_{j} + \text{Error}(\tau\beta\delta)_{ijl} + \gamma_{k} + (\tau\gamma)_{ik} \]

Dónde:

\(Y_{ijkl}\) = Valor observado de la variable respuesta.

\(\hat{Y}_{ijkl}\) = Valor ajustado de la variable respuesta.

\(\mu\) = Promedio observado de la variable respuesta.

\(\tau_{i}\) = Efecto del i-ésimo nivel del factor A.

\(\beta_{j}\) = Efecto del j-ésimo nivel del factor B.

\(\gamma_{k}\) = Efecto del k-ésimo nivel del factor C.

\(\delta_{l}\) = Efecto del l-ésimo nivel del factor Bloque.

\((\tau\gamma)_{ik}\) = Efecto de interacción del factor A x factor C dentro de los niveles ik.

\(\text{Error}(\tau\delta)_{il}\) = Residuo observado del modelo a nivel de parcelas principales.

\(\text{Error}(\tau\beta\delta)_{ijl}\) = Residuo observado del modelo a nivel de subparcelas.

\(\epsilon_{ijkl}\) = Residuo observado del modelo a nivel de subsubparcelas.

Pruebas de hipótesis

Para el factor A (Nitrógeno):

\(H_0: \tau_{A1} = \tau_{A2} = \tau_{A3} = \tau_{A4} = \tau_{A5} = 0\)

\(H_1: \text{En al menos un nivel del factor A el } \tau \text{ es diferente a los demás.}\)

\(H_1: \tau_i \neq 0\text{; en al menos un nivel del factor A.}\)

Para el factor B (Manejo):

\(H_0: \beta_{B1} = \beta_{B2} = \beta_{B3} = 0\)

\(H_1: \text{En al menos un nivel del factor B el } \beta \text{ es diferente a los demás.}\)

\(H_1: \beta_j \neq 0\text{; en al menos un nivel del factor B.}\)

Para el factor C (Variedad):

\(H_0: \gamma_{B1} = \gamma_{B2} = \gamma_{B3} = 0\)

\(H_1: \text{En al menos un nivel del factor C el } \gamma \text{ es diferente a los demás.}\)

\(H_1: \gamma_k \neq 0\text{; en al menos un nivel del factor C.}\)

Para la interacción entre factor A y factor C:

\(H_0: (\tau\gamma)_{A1C1} = (\tau\gamma)_{A1C2} = (\tau\gamma)_{A1C3} = (\tau\gamma)_{A2C1} = (\tau\gamma)_{A2C2} = ... = (\tau\gamma)_{A5C3} = 0\)

\(H_1: \text{En al menos una interacción entre el factor A y el factor C el } (\tau\gamma) \text{ es diferente a los demás.}\)

\(H_1: (\tau\gamma)_{ik} \neq 0\text{; en al menos una interacción entre el factor A y el factor C.}\)

Precaución

  • Si se ignora el diseño experimental, se obtienen los siguientes resultados, incorrectos. Observe que los grados de libertad del error es mayor, lo que facilita la detección de diferencias que en realidad no existen.
anova(modelo.dbca, test = "F")
Analysis of Variance Table

Response: rdto
                        Df  Sum Sq Mean Sq  F value    Pr(>F)    
nitrogeno                4  61.641  15.410  33.0660 2.899e-16 ***
variedad                 2 206.013 103.007 221.0235 < 2.2e-16 ***
manejo                   2  42.936  21.468  46.0645 4.892e-14 ***
bloque                   2   0.732   0.366   0.7853 0.4594531    
nitrogeno:variedad       8  14.145   1.768   3.7938 0.0008092 ***
nitrogeno:bloque         8   4.451   0.556   1.1939 0.3132682    
nitrogeno:manejo:bloque 28   6.339   0.226   0.4858 0.9830527    
Residuals               80  37.283   0.466                       
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Importante

Necesitamos especificar correctamente el término de error para el factor A. Debe tenerse en cuenta que la forma del Error es “Error(A:parcelagrande)” en el caso de efectos aleatorios o “Error(A:bloque)” para el caso de efectos fijos y puede cambiar dependiendo de la disposición de los datos. La clave es conocer los grados de libertad correcto para saber que se obtienen los resultados correctos.

aov(rdto ~ nitrogeno * variedad + manejo + bloque + Error(bloque/nitrogeno/manejo), data = data) -> aov.dbca
summary(aov.dbca)

Error: bloque
       Df Sum Sq Mean Sq
bloque  2  0.732   0.366

Error: bloque:nitrogeno
          Df Sum Sq Mean Sq F value   Pr(>F)    
nitrogeno  4  61.64  15.410    27.7 9.73e-05 ***
Residuals  8   4.45   0.556                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Error: bloque:nitrogeno:manejo
          Df Sum Sq Mean Sq F value  Pr(>F)    
manejo     2  42.94  21.468   94.82 3.4e-13 ***
Residuals 28   6.34   0.226                    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Error: Within
                   Df Sum Sq Mean Sq F value   Pr(>F)    
variedad            2 206.01  103.01 221.023  < 2e-16 ***
nitrogeno:variedad  8  14.14    1.77   3.794 0.000809 ***
Residuals          80  37.28    0.47                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
data %>% with(agricolae::ssp.plot(block = bloque,
                                  pplot = nitrogeno,
                                  splot = manejo,
                                  ssplot = variedad,
                                  Y = rdto))

ANALYSIS SPLIT-SPLIT PLOT:  rdto 
Class level information

nitrogeno   :  0 50 80 110 140 
manejo  :  m1 m2 m3 
variedad    :  1 2 3 
bloque  :  1 2 3 

Number of observations:  135 

Analysis of Variance Table

Response: rdto
                          Df  Sum Sq Mean Sq  F value    Pr(>F)    
bloque                     2   0.732   0.366      NaN       NaN    
nitrogeno                  4  61.641  15.410  27.6953 9.734e-05 ***
Ea                         8   4.451   0.556                       
manejo                     2  42.936  21.468  81.9965 2.303e-10 ***
nitrogeno:manejo           8   1.103   0.138   0.5266  0.822648    
Eb                        20   5.236   0.262                       
variedad                   2 206.013 103.007 207.8667 < 2.2e-16 ***
variedad:nitrogeno         8  14.145   1.768   3.5679  0.001916 ** 
variedad:manejo            4   3.852   0.963   1.9432  0.114899    
variedad:nitrogeno:manejo 16   3.699   0.231   0.4666  0.953759    
Ec                        60  29.732   0.496                       
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

cv(a) = 11.4 %, cv(b) = 7.8 %, cv(c) = 10.7 %, Mean = 6.554415 
broom::tidy(aov.dbca)
# A tibble: 8 × 7
  stratum                 term            df   sumsq  meansq statistic   p.value
  <chr>                   <chr>        <dbl>   <dbl>   <dbl>     <dbl>     <dbl>
1 bloque                  bloque           2   0.732   0.366     NA    NA       
2 bloque:nitrogeno        nitrogeno        4  61.6    15.4       27.7   9.73e- 5
3 bloque:nitrogeno        Residuals        8   4.45    0.556     NA    NA       
4 bloque:nitrogeno:manejo manejo           2  42.9    21.5       94.8   3.40e-13
5 bloque:nitrogeno:manejo Residuals       28   6.34    0.226     NA    NA       
6 Within                  variedad         2 206.    103.       221.    2.60e-33
7 Within                  nitrogeno:v…     8  14.1     1.77       3.79  8.09e- 4
8 Within                  Residuals       80  37.3     0.466     NA    NA       

Valor de la tabla de F para el factor A con una significancia de 0.05.

qf(0.95, 4, 8)
[1] 3.837853

Valor de la tabla de F para el factor B con una significancia de 0.05.

qf(0.95, 2, 28)
[1] 3.340386

Valor de la tabla de F para la interacción A:B con una significancia de 0.05.

qf(0.95, 2, 80)
[1] 3.110766

Conclusión.

Con respecto al Factor A: A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos un nivel del factor A tiene un efecto estadísticamente distinto de 0.

Con respecto al Factor B: A un nivel de significancia de 0.05, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos un nivel del factor B tiene un efecto estadísticamente distinto de 0.

Con respecto al Factor C: A un nivel de significancia de 0.05, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos un nivel del factor C tiene un efecto estadísticamente distinto de 0.

Con respecto a la interacción entre el Factor A y Factor C: A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos una interacción entre un nivel del factor A y un nivel del factor C existe un efecto de antagonismo o sinergismo sobre el rendimiento.

get_df_ea_spspplot <- function(object, name_FA) {
  library(broom)
  tidy_aov <- broom::tidy(object)
  df_rep_A_residuals <- tidy_aov %>% 
    dplyr::filter(endsWith(stratum, paste0(":",name_FA)) & 
                    term == "Residuals") %>%
    dplyr::pull(df)
  return(df_rep_A_residuals)
}
get_df_ea_spspplot(aov.dbca, "nitrogeno")
[1] 8
get_mse_ea_spspplot <- function(object, name_FA) {
  library(broom)
  tidy_aov <- broom::tidy(object)
  meansq_rep_A_residuals <- tidy_aov %>% 
    dplyr::filter(endsWith(stratum, paste0(":",name_FA)) & 
                    term == "Residuals") %>%
    dplyr::pull(meansq)
  return(meansq_rep_A_residuals)
}
get_mse_ea_spspplot(aov.dbca, "nitrogeno")
[1] 0.5564188
get_df_eb_spspplot <- function(object, name_FA, name_FB) {
  library(broom)
  tidy_aov <- broom::tidy(object)
  df_rep_B_residuals <- tidy_aov %>% 
    dplyr::filter(grepl(paste0(name_FA,":",name_FB), stratum) & 
                    term == "Residuals") %>%
    dplyr::pull(df)
  return(df_rep_B_residuals)
}
get_df_eb_spspplot(aov.dbca, "nitrogeno", "manejo")
[1] 28
get_mse_eb_spspplot <- function(object, name_FA, name_FB) {
  library(broom)
  tidy_aov <- broom::tidy(object)
  meansq_rep_B_residuals <- tidy_aov %>% 
    dplyr::filter(grepl(paste0(name_FA,":",name_FB), stratum) & 
                    term == "Residuals") %>%
    dplyr::pull(meansq)
  return(meansq_rep_B_residuals)
}
get_mse_eb_spspplot(aov.dbca, "nitrogeno", "manejo")
[1] 0.2264039
agricolae::cv.model(modelo.dbca)
[1] 10.41548
cv.a <- sqrt(get_mse_ea_spspplot(aov.dbca, "nitrogeno"))*100/mean(data$rdto)
cv.a
[1] 11.38065
cv.b <- sqrt(get_mse_eb_spspplot(aov.dbca, "nitrogeno", "manejo"))*100/mean(data$rdto)
cv.b
[1] 7.259521
cv.c <- sqrt(dvmisc::get_mse(modelo.dbca))*100/mean(data$rdto)
cv.c
[1] 10.41548

Comparaciones de medias para los efectos principales del Factor A

data %>% with(LSD.test(
  rdto, # Cambiar según nombre de variable respuesta
  nitrogeno, # Cambiar según nombre de variable independiente
  DFerror = get_df_ea_spspplot(aov.dbca, "nitrogeno"), 
  MSerror = get_mse_ea_spspplot(aov.dbca, "nitrogeno"),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: rdto ~ nitrogeno

LSD t Test for rdto 

Mean Square Error:  0.5564188 

nitrogeno,  means and individual ( 95 %) CI

        rdto      std  r      LCL      UCL   Min    Max
0   5.384704 1.206963 27 5.053665 5.715743 3.320  8.020
110 6.937370 1.474547 27 6.606331 7.268409 4.246  9.660
140 7.233926 1.968153 27 6.902887 7.564965 3.132 10.360
50  6.220333 1.615861 27 5.889294 6.551372 3.188  9.942
80  6.995741 1.371302 27 6.664702 7.326780 4.422  9.320

Alpha: 0.05 ; DF Error: 8
Critical Value of t: 2.306004 

least Significant Difference: 0.4681598 

Treatments with the same letter are not significantly different.

        rdto groups
140 7.233926      a
80  6.995741      a
110 6.937370      a
50  6.220333      b
0   5.384704      c

Comparaciones de medias para los efectos principales del Factor B

data %>% with(LSD.test(
  rdto, # Cambiar según nombre de variable respuesta
  manejo, # Cambiar según nombre de variable independiente
  DFerror = get_df_eb_spspplot(aov.dbca, "nitrogeno", "manejo"), 
  MSerror = get_mse_eb_spspplot(aov.dbca, "nitrogeno", "manejo"),
  alpha = 0.05,
  group = TRUE,
  main = NULL,
  console=TRUE))

Study: rdto ~ manejo

LSD t Test for rdto 

Mean Square Error:  0.2264039 

manejo,  means and individual ( 95 %) CI

       rdto      std  r      LCL      UCL   Min    Max
m1 5.900378 1.486531 45 5.755082 6.045673 3.132  9.314
m2 6.486156 1.621936 45 6.340860 6.631451 3.625  9.680
m3 7.276711 1.635020 45 7.131416 7.422007 4.225 10.360

Alpha: 0.05 ; DF Error: 28
Critical Value of t: 2.048407 

least Significant Difference: 0.2054788 

Treatments with the same letter are not significantly different.

       rdto groups
m3 7.276711      a
m2 6.486156      b
m1 5.900378      c

Comparaciones de medias para los efectos principales del Factor C

data %>% with(LSD.test(
  rdto, # Cambiar según nombre de variable respuesta
  variedad, # Cambiar según nombre de variable independiente
  DFerror = df.residual(modelo.dbca), 
  MSerror = dvmisc::get_mse(modelo.dbca),
  alpha = 0.05,
  group = TRUE,
  main = NULL,
  console=TRUE))

Study: rdto ~ variedad

LSD t Test for rdto 

Mean Square Error:  0.4660436 

variedad,  means and individual ( 95 %) CI

      rdto      std  r      LCL      UCL   Min    Max
1 5.126822 0.971530 45 4.924299 5.329345 3.132  7.309
2 6.396133 1.065752 45 6.193611 6.598656 4.166  8.950
3 8.140289 1.314438 45 7.937766 8.342812 5.244 10.360

Alpha: 0.05 ; DF Error: 80
Critical Value of t: 1.990063 

least Significant Difference: 0.2864105 

Treatments with the same letter are not significantly different.

      rdto groups
3 8.140289      a
2 6.396133      b
1 5.126822      c

Precaución

Si el análisis de varianza arroja que los niveles de un factor son estadísticamente similares entre sí, entonces no es necesario realizar una prueba de comparación de medias y por ende todos estos niveles pertenecen a un mismo grupo de significancia “a”.

Comparaciones de medias para las interacciones FAxFB

Para los niveles del factor A dentro del nivel B1:

  • A1 vs A2:

\(H_0: \mu_{A1} - \mu_{A2} = 0\)

\(H_1: \mu_{A1} - \mu_{A2} \neq 0\)

  • A1 vs A3:

\(H_0: \mu_{A1} - \mu_{A3} = 0\)

\(H_1: \mu_{A1} - \mu_{A3} \neq 0\)

“…”

  • A4 vs A5:

\(H_0: \mu_{A4} - \mu_{A5} = 0\)

\(H_1: \mu_{A4} - \mu_{A5} \neq 0\)

Para los niveles del factor B dentro del nivel A1:

  • B1 vs B2:

\(H_0: \mu_{B1} - \mu_{B2} = 0\)

\(H_1: \mu_{B1} - \mu_{B2} \neq 0\)

  • B1 vs B3:

\(H_0: \mu_{B1} - \mu_{B3} = 0\)

\(H_1: \mu_{B1} - \mu_{B3} \neq 0\)

  • B2 vs B3:

\(H_0: \mu_{B2} - \mu_{B3} = 0\)

\(H_1: \mu_{B2} - \mu_{B3} \neq 0\)

NOTA: Repetir este proceso para cada nivel de A y cada nivel de B.

datasp <- data %>%
  group_by(bloque, nitrogeno, manejo) %>%
  summarise(rdto = mean(rdto, na.rm = T)) %>%
  ungroup()

slice_head(datasp, n = 5) %>% gt()
bloque nitrogeno manejo rdto
1 0 m1 4.925333
1 0 m2 5.434667
1 0 m3 6.083667
1 50 m1 5.163000
1 50 m2 6.191333
modelosp <- lm(rdto ~ bloque + nitrogeno/manejo + bloque%in%nitrogeno, data = datasp)
phia::testInteractions(modelosp,
                       fixed = "nitrogeno",
                       across = "manejo",
                       adjustment = "none")
F Test: 
P-value adjustment method: none
          manejo1  manejo2 Df Sum of Sq      F    Pr(>F)    
  0       -1.2316 -0.93033  2    2.4730 14.168 0.0001471 ***
 50       -1.3017 -0.87733  2    2.6441 15.149 9.882e-05 ***
 80       -1.2947 -0.74111  2    2.5318 14.505 0.0001281 ***
110       -1.5501 -0.64311  2    3.6391 20.849 1.281e-05 ***
140       -1.5037 -0.76089  2    3.3917 19.432 2.050e-05 ***
Residuals                  20    1.7454                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
phia::testInteractions(modelosp,
                       fixed = "manejo",
                       across = "nitrogeno",
                       adjustment = "none")
F Test: 
P-value adjustment method: none
          nitrogeno1 nitrogeno2 nitrogeno3 nitrogeno4 Df Sum of Sq      F
m1           -1.6113   -0.84011   -0.10544   -0.36678  4    5.2148 14.938
m2           -2.0529   -1.15856   -0.29467   -0.20256  4    8.8009 25.211
m3           -1.8834   -1.04211   -0.31444   -0.32033  4    6.8990 19.763
Residuals                                             20    1.7454       
             Pr(>F)    
m1        8.353e-06 ***
m2        1.441e-07 ***
m3        1.012e-06 ***
Residuals              
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Precaución

Este arreglo no funciona si es que no se tiene un cálculo de promedios de rendimiento a nivel de sub-parcela

Caso: Evaluación del rendimiento del maíz según dos niveles de estrés hídrico, 3 dosis de bioestimulante y dos hibridos mejorados.

archivos <- list.files(pattern = "datos split split plot.xlsx", 
                       full.names = TRUE,
                       recursive = TRUE)

# Importación
data2 <- readxl::read_xlsx(archivos,
                           sheet = "ej2")

# Preprocesamiento

data2 <- data2 %>%
  mutate_if(is.character, factor) %>%
  mutate(Bloque = factor(Bloque),
         Plot = factor(Plot),
         Splot = factor(Splot))
datasp2 <- data2 %>%
  group_by(Splot) %>%
  mutate(Rend = mean(Rend, na.rm = T)) %>%
  ungroup() %>%
  group_by(Bloque, Condición, Dosis) %>%
  summarise(Rend = mean(Rend, na.rm = T)) %>%
  ungroup()

slice_head(datasp2, n = 5) %>% gt()
Bloque Condición Dosis Rend
I C0 D0 9557.946
I C0 D1 9680.578
I C0 D2 11840.612
I C0 D3 10844.880
I C1 D0 7739.343
modelo.dbca.ej2 <- lm(Rend ~ Condición * Dosis * Híbrido + Bloque + Bloque/Condición/Híbrido, data = data2)
aov(Rend ~ Condición * Dosis * Híbrido + Bloque + Error(Bloque/Condición/Dosis), data = data2) -> aov.dbca.ej2

aov.dbca.ej2 %>% broom::tidy()
# A tibble: 11 × 7
   stratum                term               df  sumsq meansq statistic  p.value
   <chr>                  <chr>           <dbl>  <dbl>  <dbl>     <dbl>    <dbl>
 1 Bloque                 Bloque              2 8.58e5 4.29e5     NA    NA      
 2 Bloque:Condición       Condición           1 6.07e7 6.07e7    533.    1.87e-3
 3 Bloque:Condición       Residuals           2 2.27e5 1.14e5     NA    NA      
 4 Bloque:Condición:Dosis Dosis               3 4.21e7 1.40e7     96.4   1.15e-8
 5 Bloque:Condición:Dosis Condición:Dosis     3 1.91e6 6.35e5      4.36  2.70e-2
 6 Bloque:Condición:Dosis Residuals          12 1.75e6 1.46e5     NA    NA      
 7 Within                 Híbrido             1 8.49e7 8.49e7     92.5   4.73e-8
 8 Within                 Condición:Híbr…     1 9.36e7 9.36e7    102.    2.41e-8
 9 Within                 Dosis:Híbrido       3 4.58e6 1.53e6      1.66  2.15e-1
10 Within                 Condición:Dosi…     3 8.44e6 2.81e6      3.07  5.81e-2
11 Within                 Residuals          16 1.47e7 9.18e5     NA    NA      
modelosp.ej2 <- lm(Rend ~ Bloque + Bloque %in% Condición + Condición:Dosis, data = datasp2)
phia::testInteractions(modelosp.ej2,
                       fixed = "Condición",
                       across = "Dosis",
                       adjustment = "none")
F Test: 
P-value adjustment method: none
           Dosis1  Dosis2  Dosis3 Df Sum of Sq      F    Pr(>F)    
C0        -1309.3 -1380.1 1379.88  3  15283150 69.900 7.201e-08 ***
C1         -874.5 -1148.8  752.75  3   6742764 30.839 6.378e-06 ***
Residuals                         12    874569                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
phia::testInteractions(modelosp.ej2,
                       fixed = "Dosis",
                       across = "Condición",
                       adjustment = "none")
F Test: 
P-value adjustment method: none
           Value Df Sum of Sq       F    Pr(>F)    
D0        1823.3  1   4986898  68.425 2.666e-06 ***
D1        2026.9  1   6162333  84.554 8.796e-07 ***
D2        2885.3  1  12487438 171.341 1.826e-08 ***
D3        2258.2  1   7648991 104.952 2.757e-07 ***
Residuals        12    874569                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Comparaciones de medias de los niveles de B dentro de cada nivel de A

FA_A1 <- data2 %>% filter(Condición=="C0")
FA_A2 <- data2 %>% filter(Condición=="C1")

fcomp1 <- function(x){
  comp <- LSD.test(x$Rend, # Cambiar según nombre de variable respuesta
                   x$Dosis, # Cambiar según nombre de variable independiente
                   DFerror = get_df_eb_spspplot(aov.dbca.ej2, "Condición", "Dosis"), 
                   MSerror = get_mse_eb_spspplot(aov.dbca.ej2, "Condición", "Dosis"),
                   alpha = 0.05,
                   group=TRUE,
                   main = NULL,
                   console=FALSE)
  return(comp[[5]] %>%
           rename("Rend" = "x$Rend") # Cambiar según nombre de variable respuesta
         )
}

Comparaciones de medias de los niveles de B dentro de cada nivel de A

fcomp1(FA_A1)
        Rend groups
D2 12113.510      a
D3 10733.627      b
D0  9424.306      c
D1  9353.512      c

Comparaciones de los niveles de B dentro del nivel A2

fcomp1(FA_A2)
       Rend groups
D2 9228.209      a
D3 8475.458      b
D0 7600.958      c
D1 7326.637      c

Forma más rápida

filter_by_factor_level <- function(data, factor_name) {
  levels <- levels(data[[deparse(substitute(factor_name))]])
  filters <- purrr::map(levels, ~ filter(data, {{factor_name}} == .x))
  names(filters) <- levels
  filters
}
datos_filtrados <- filter_by_factor_level(data2, Condición)
LSD.test.multcomp <- function(df, respuesta, independiente, plot, splot, aov){
  comp <- LSD.test(df[[respuesta]],
                   df[[independiente]],
                   DFerror = get_df_eb_spspplot(aov, plot, splot), 
                   MSerror = get_mse_eb_spspplot(aov, plot, splot),
                   alpha = 0.05,
                   group=TRUE,
                   main = NULL,
                   console=FALSE)
  return(comp[[5]] %>%
           rename("y" = "df[[respuesta]]")
         )
}
resultados <- purrr::map(datos_filtrados,
                         ~LSD.test.multcomp(
                           .x,
                           respuesta = "Rend",
                           independiente ="Dosis",
                           plot = "Condición",
                           splot = "Dosis",
                           aov = aov.dbca.ej2))
resultados
$C0
           y groups
D2 12113.510      a
D3 10733.627      b
D0  9424.306      c
D1  9353.512      c

$C1
          y groups
D2 9228.209      a
D3 8475.458      b
D0 7600.958      c
D1 7326.637      c

Comparaciones de medias de los niveles de A dentro de cada nivel de B

FB_B1 <- data2 %>% filter(Dosis=="D0")
FB_B2 <- data2 %>% filter(Dosis=="D1")
FB_B3 <- data2 %>% filter(Dosis=="D2")
FB_B4 <- data2 %>% filter(Dosis=="D3")

fcomp2 <- function(x){
  comp <- LSD.test(x$Rend, # Cambiar según nombre de variable respuesta
                   x$Condición, # Cambiar según nombre de variable independiente
                   DFerror = get_df_eb_spspplot(aov.dbca.ej2, "Condición", "Dosis"), 
                   MSerror = get_mse_eb_spspplot(aov.dbca.ej2, "Condición", "Dosis"),
                   alpha = 0.05,
                   group=TRUE,
                   main = NULL,
                   console=FALSE)
  return(comp[[5]] %>%
           rename("Rend" = "x$Rend") # Cambiar según nombre de variable respuesta
         )
}

Comparaciones de los niveles de A dentro del nivel B1

fcomp2(FB_B1)
       Rend groups
C0 9424.306      a
C1 7600.958      b

Comparaciones de los niveles de A dentro del nivel B2

fcomp2(FB_B2)
       Rend groups
C0 9353.512      a
C1 7326.637      b

Comparaciones de los niveles de A dentro del nivel B3

fcomp2(FB_B3)
        Rend groups
C0 12113.510      a
C1  9228.209      b

Comparaciones de los niveles de A dentro del nivel B4

fcomp2(FB_B4)
        Rend groups
C0 10733.627      a
C1  8475.458      b

Forma más rápida

datos_filtrados <- filter_by_factor_level(data2, Dosis)
resultados <- purrr::map(datos_filtrados,
                         ~LSD.test.multcomp(
                           .x,
                           respuesta = "Rend",
                           independiente ="Condición",
                           plot = "Condición",
                           splot = "Dosis",
                           aov = aov.dbca.ej2))
resultados
$D0
          y groups
C0 9424.306      a
C1 7600.958      b

$D1
          y groups
C0 9353.512      a
C1 7326.637      b

$D2
           y groups
C0 12113.510      a
C1  9228.209      b

$D3
           y groups
C0 10733.627      a
C1  8475.458      b

Varios test en una sola función

multcomp.test <- function(df, respuesta, independiente, test, plot, splot, aov){
  if (test == "LSD") {
    comp <- LSD.test(df[[respuesta]],
                     df[[independiente]],
                     DFerror = get_df_eb_spspplot(aov, plot, splot), 
                     MSerror = get_mse_eb_spspplot(aov, plot, splot),
                     alpha = 0.05,
                     group=TRUE,
                     main = NULL,
                     console=FALSE)[[5]]
  } else if (test == "HSD") {
    comp <- HSD.test(df[[respuesta]],
                     df[[independiente]],
                     DFerror = get_df_eb_spspplot(aov, plot, splot), 
                     MSerror = get_mse_eb_spspplot(aov, plot, splot),
                     alpha = 0.05,
                     group=TRUE,
                     main = NULL,
                     console=FALSE)[[5]]
  } else if (test == "duncan") {
    comp <- duncan.test(df[[respuesta]],
                     df[[independiente]],
                     DFerror = get_df_eb_spspplot(aov, plot, splot), 
                     MSerror = get_mse_eb_spspplot(aov, plot, splot),
                     alpha = 0.05,
                     group=TRUE,
                     main = NULL,
                     console=FALSE)[[6]]
  } else if (test == "SNK") {
    comp <- SNK.test(df[[respuesta]],
                     df[[independiente]],
                     DFerror = get_df_eb_spspplot(aov, plot, splot), 
                     MSerror = get_mse_eb_spspplot(aov, plot, splot),
                     alpha = 0.05,
                     group=TRUE,
                     main = NULL,
                     console=FALSE)[[6]]
  } else {
    stop("Test no válido. Los tests disponibles son LSD, HSD, duncan, y SNK.")
  }
  
  return(comp %>%
           rename("y" = "df[[respuesta]]")
         )
}

Comparación de los niveles del factor A dentro de cada nivel del factor B

resultados <- purrr::map(datos_filtrados,
                         ~multcomp.test(
                           .x,
                           respuesta = "Rend",
                           independiente = "Condición",
                           plot = "Condición",
                           splot = "Dosis",
                           aov = aov.dbca.ej2,
                           test = "SNK"))
resultados
$D0
          y groups
C0 9424.306      a
C1 7600.958      b

$D1
          y groups
C0 9353.512      a
C1 7326.637      b

$D2
           y groups
C0 12113.510      a
C1  9228.209      b

$D3
           y groups
C0 10733.627      a
C1  8475.458      b

Comparación de los niveles del factor B dentro de cada nivel del factor A

datos_filtrados <- filter_by_factor_level(data2, Condición)
resultados <- purrr::map(datos_filtrados,
                         ~multcomp.test(
                           .x,
                           respuesta = "Rend",
                           independiente = "Dosis",
                           plot = "Condición",
                           splot = "Dosis",
                           aov = aov.dbca.ej2,
                           test = "SNK"))
resultados
$C0
           y groups
D2 12113.510      a
D3 10733.627      b
D0  9424.306      c
D1  9353.512      c

$C1
          y groups
D2 9228.209      a
D3 8475.458      b
D0 7600.958      c
D1 7326.637      c

Última forma más automática

filter_by_2factor_level <- function(data, factor_name1, factor_name2) {
  levels1 <- levels(data[[deparse(substitute(factor_name1))]])
  filters1 <- purrr::map(levels1, ~ filter(data, {{factor_name1}} == .x))
  names(filters1) <- levels1
  
  levels2 <- levels(data[[deparse(substitute(factor_name2))]])
  filters2 <- purrr::map(levels2, ~ filter(data, {{factor_name2}} == .x))
  names(filters2) <- levels2
  
  result <- list()
  result[[deparse(substitute(factor_name1))]] <- filters1
  result[[deparse(substitute(factor_name2))]] <- filters2
  return(result)
}
datos_filtrados <- filter_by_2factor_level(data = data2,
                       factor_name1 = Condición,
                       factor_name2 =  Dosis)
multcomp.test_2factors <- function(object, respuesta, factor_name1, factor_name2, test, plot, splot, aov){
  
  # Función auxiliar para aplicar la prueba de comparaciones múltiples a un data frame
  multcomp_df <- function(df, respuesta, factor_name, test, plot, splot, aov){
    if (test == "LSD") {
      comp <- LSD.test(df[[respuesta]],
                       df[[factor_name]],
                       DFerror = get_df_eb_spspplot(aov, plot, splot), 
                       MSerror = get_mse_eb_spspplot(aov, plot, splot),
                       alpha = 0.05,
                       group=TRUE,
                       main = NULL,
                       console=FALSE)[[5]]
    } else if (test == "HSD") {
      comp <- HSD.test(df[[respuesta]],
                       df[[factor_name]],
                       DFerror = get_df_eb_spspplot(aov, plot, splot), 
                       MSerror = get_mse_eb_spspplot(aov, plot, splot),
                       alpha = 0.05,
                       group=TRUE,
                       main = NULL,
                       console=FALSE)[[5]]
    } else if (test == "duncan") {
      comp <- duncan.test(df[[respuesta]],
                          df[[factor_name]],
                          DFerror = get_df_eb_spspplot(aov, plot, splot), 
                          MSerror = get_mse_eb_spspplot(aov, plot, splot),
                          alpha = 0.05,
                          group=TRUE,
                          main = NULL,
                          console=FALSE)[[6]]
    } else if (test == "SNK") {
      comp <- SNK.test(df[[respuesta]],
                       df[[factor_name]],
                       DFerror = get_df_eb_spspplot(aov, plot, splot), 
                       MSerror = get_mse_eb_spspplot(aov, plot, splot),
                       alpha = 0.05,
                       group=TRUE,
                       main = NULL,
                       console=FALSE)[[6]]
    } else {
      stop("Test no válido. Los tests disponibles son LSD, HSD, duncan, y SNK.")
    }
    
    return(comp %>%
             rename("y" = "df[[respuesta]]")
           )
  }
  
  # Aplicar la prueba de comparaciones múltiples a todos los data frames dentro de filters1
  comp_filters1 <- lapply(object[[1]], function(df){
    multcomp_df(df, respuesta, factor_name2, test, plot, splot, aov) %>%
      arrange(row.names(.)) %>%
      rownames_to_column(var = "x") %>%
      relocate(x)
  })
  
  # Aplicar la prueba de comparaciones múltiples a todos los data frames dentro de filters2
  comp_filters2 <- lapply(object[[2]], function(df){
    multcomp_df(df, respuesta, factor_name1, test, plot, splot, aov) %>%
      dplyr::arrange(row.names(.)) %>%
      rownames_to_column(var = "x") %>%
      relocate(x) %>%
      dplyr::mutate(groups = toupper(groups))
  })
  
  row.names(comp_filters1) <- NULL
  row.names(comp_filters2) <- NULL
  # Retornar una lista con las comparaciones múltiples para cada data frame
  result <- list()
  result[[as.name(substitute(factor_name1))]] <- comp_filters1
  result[[as.name(substitute(factor_name2))]] <- comp_filters2
  return(#list(#"Comparación de los niveles del factor B dentro de cada nivel del factor A",
         result#[[1]],
         # "Comparación de los niveles del factor A dentro de cada nivel del factor B",
         # result[[2]]
         # )
  )
}
multcomp.test_2factors(
  object = datos_filtrados,
  respuesta = "Rend",
  factor_name1 = "Condición",
  factor_name2 = "Dosis",
  test = "duncan",
  plot = "Condición",
  splot = "Dosis",
  aov = aov.dbca.ej2) -> result.comp
result.comp
$Condición
$Condición$C0
   x         y groups
1 D0  9424.306      c
2 D1  9353.512      c
3 D2 12113.510      a
4 D3 10733.627      b

$Condición$C1
   x        y groups
1 D0 7600.958      c
2 D1 7326.637      c
3 D2 9228.209      a
4 D3 8475.458      b


$Dosis
$Dosis$D0
   x        y groups
1 C0 9424.306      A
2 C1 7600.958      B

$Dosis$D1
   x        y groups
1 C0 9353.512      A
2 C1 7326.637      B

$Dosis$D2
   x         y groups
1 C0 12113.510      A
2 C1  9228.209      B

$Dosis$D3
   x         y groups
1 C0 10733.627      A
2 C1  8475.458      B
# Convertir la lista a un data frame
df <- result.comp %>%
  reshape2::melt() %>% 
  ungroup() %>%
  dplyr::select(-variable) %>%
  relocate("Factor" = "L1",
           "Nivel" = "L2",
           x,
           "y" = "value",
           groups)
df
      Factor Nivel  x         y groups
1  Condición    C0 D0  9424.306      c
2  Condición    C0 D1  9353.512      c
3  Condición    C0 D2 12113.510      a
4  Condición    C0 D3 10733.627      b
5  Condición    C1 D0  7600.958      c
6  Condición    C1 D1  7326.637      c
7  Condición    C1 D2  9228.209      a
8  Condición    C1 D3  8475.458      b
9      Dosis    D0 C0  9424.306      A
10     Dosis    D0 C1  7600.958      B
11     Dosis    D1 C0  9353.512      A
12     Dosis    D1 C1  7326.637      B
13     Dosis    D2 C0 12113.510      A
14     Dosis    D2 C1  9228.209      B
15     Dosis    D3 C0 10733.627      A
16     Dosis    D3 C1  8475.458      B
# función que filtra por los dos niveles especificados por el usuario y devuelve dos subconjuntos de datos
create_report <- function(df, level1, level2) {
  
  # filtrar por el primer nivel
  subset1 <- df %>% filter(Factor == level1) %>%
    rename(!!level2 := x,
           !!level1 := Nivel) %>%
    dplyr::select(-c(Factor))
  
  # filtrar por el segundo nivel
  subset2 <- df %>% filter(Factor == level2) %>%
    rename(!!level1 := x,
           !!level2 := Nivel) %>%
    dplyr::select(-c(Factor,y))
  
  df <- subset1 %>% 
    dplyr::left_join(subset2,
              by = c(level1,level2)) %>%
    dplyr::mutate(groups = paste0(groups.y,groups.x)) %>%
    dplyr::select(!!level1,!!level2, y, groups)
  
  # devolver una lista con los dos subconjuntos
  return(df)
}
df2 <- create_report(df = df,
               level1 = "Condición",
               level2 = "Dosis") 
df2 %>% gt()
Condición Dosis y groups
C0 D0 9424.306 Ac
C0 D1 9353.512 Ac
C0 D2 12113.510 Aa
C0 D3 10733.627 Ab
C1 D0 7600.958 Bc
C1 D1 7326.637 Bc
C1 D2 9228.209 Ba
C1 D3 8475.458 Bb
df2 %>% 
  dplyr::mutate(y = round(y,2)) %>%
 pivot_wider(names_from = Dosis, values_from = c(y, groups), 
             names_glue = "{Dosis}_{.value}") %>% 
  dplyr::select(Condición, D0_y, D0_groups, D1_y, D1_groups, D2_y, D2_groups, D3_y, D3_groups) %>% gt()
Condición D0_y D0_groups D1_y D1_groups D2_y D2_groups D3_y D3_groups
C0 9424.31 Ac 9353.51 Ac 12113.51 Aa 10733.63 Ab
C1 7600.96 Bc 7326.64 Bc 9228.21 Ba 8475.46 Bb
# función que filtra por los dos niveles especificados por el usuario y devuelve dos subconjuntos de datos
create_report <- function(df, level1, level2) {
  
  # filtrar por el primer nivel
  subset1 <- df %>% filter(Factor == level1) %>%
    rename(!!level2 := x,
           !!level1 := Nivel) %>%
    dplyr::select(-c(Factor))
  
  # filtrar por el segundo nivel
  subset2 <- df %>% filter(Factor == level2) %>%
    rename(!!level1 := x,
           !!level2 := Nivel) %>%
    dplyr::select(-c(Factor,y))
  
  df <- subset1 %>% 
    dplyr::left_join(subset2,
              by = c(level1,level2)) %>%
    dplyr::mutate(y = paste0(round(y,2), " ", groups.y, groups.x)) %>%
    dplyr::select(!!level1,!!level2, y)
  
  # devolver una lista con los dos subconjuntos
  return(df)
}
df3 <- create_report(df = df,
               level1 = "Condición",
               level2 = "Dosis") 
df3 %>% gt()
Condición Dosis y
C0 D0 9424.31 Ac
C0 D1 9353.51 Ac
C0 D2 12113.51 Aa
C0 D3 10733.63 Ab
C1 D0 7600.96 Bc
C1 D1 7326.64 Bc
C1 D2 9228.21 Ba
C1 D3 8475.46 Bb
df3 %>% 
 pivot_wider(names_from = Dosis,
             values_from = c(y), 
             names_glue = "{Dosis}") %>%
  gt()
Condición D0 D1 D2 D3
C0 9424.31 Ac 9353.51 Ac 12113.51 Aa 10733.63 Ab
C1 7600.96 Bc 7326.64 Bc 9228.21 Ba 8475.46 Bb

Diseño de bloques completos al azar en arreglo de bloques divididos

Planeamiento


Crear un libro de campo con el paquete agricolae


FA <- c("A1","A2","A3")
FB <- c("B1","B2")

r <- 6

salida <- agricolae::design.strip(trt1 = FA,
                                  trt2 = FB,
                                  r = r,
                                  serie = 3,
                                  seed = 123,
                                  kinds = "Super-Duper",
                                  randomization = TRUE)
book <- salida$book

Sketch del diseño para FA

distribuir_vector_matriz <- function(vector, niveles_FA, niveles_FB, num_bloques) {
  # Verificar que el número de niveles de FB sea menor o igual a la mitad del número de bloques
  stopifnot(niveles_FB <= num_bloques/2)
  
  # Calcular el número de columnas por bloque
  columnas_bloque <- niveles_FA
  
  # Calcular el número de filas por bloque
  filas_bloque <- niveles_FB
  
  # Calcular el número total de filas
  num_filas <- num_bloques * filas_bloque
  
  # Calcular el número de bloques completos
  num_bloques_completos <- num_filas %/% filas_bloque
  
  # Crear una matriz vacía
  matriz <- matrix(NA, nrow = num_filas, ncol = columnas_bloque)
  
  # Distribuir los valores en la matriz
  for (i in 1:num_bloques_completos) {
    inicio_fila <- (i - 1) * filas_bloque + 1
    fin_fila <- i * filas_bloque
    inicio_vector <- (i - 1) * columnas_bloque * filas_bloque + 1
    fin_vector <- i * columnas_bloque * filas_bloque
    matriz[inicio_fila:fin_fila, ] <- matrix(vector[inicio_vector:fin_vector], nrow = filas_bloque, byrow = TRUE) %>% t()
  }
  
  # Manejar los bloques incompletos
  if (num_filas %% filas_bloque != 0) {
    inicio_fila <- num_bloques_completos * filas_bloque + 1
    fin_fila <- num_filas
    inicio_vector <- num_bloques_completos * columnas_bloque * filas_bloque + 1
    fin_vector <- length(vector)
    matriz[inicio_fila:fin_fila, ] <- matrix(vector[inicio_vector:fin_vector], nrow = fin_fila - inicio_fila + 1, byrow = TRUE)
  }
  
  return(matriz)
}
distribuir_vector_matriz(
  vector = book$FA,
  niveles_FA = length(levels(book$FA)),
  niveles_FB = length(levels(book$FB)),
  num_bloques = length(levels(book$block)))
      [,1] [,2] [,3]
 [1,] "A3" "A1" "A2"
 [2,] "A3" "A1" "A2"
 [3,] "A2" "A1" "A3"
 [4,] "A2" "A1" "A3"
 [5,] "A1" "A2" "A3"
 [6,] "A1" "A2" "A3"
 [7,] "A1" "A3" "A2"
 [8,] "A1" "A3" "A2"
 [9,] "A3" "A2" "A1"
[10,] "A3" "A2" "A1"
[11,] "A3" "A1" "A2"
[12,] "A3" "A1" "A2"

Sketch del diseño para FB

distribuir_vector_matriz(
  vector = book$FB,
  niveles_FA = length(levels(book$FA)),
  niveles_FB = length(levels(book$FB)),
  num_bloques = length(levels(book$block)))
      [,1] [,2] [,3]
 [1,] "B1" "B1" "B1"
 [2,] "B2" "B2" "B2"
 [3,] "B2" "B2" "B2"
 [4,] "B1" "B1" "B1"
 [5,] "B2" "B2" "B2"
 [6,] "B1" "B1" "B1"
 [7,] "B1" "B1" "B1"
 [8,] "B2" "B2" "B2"
 [9,] "B2" "B2" "B2"
[10,] "B1" "B1" "B1"
[11,] "B1" "B1" "B1"
[12,] "B2" "B2" "B2"

Matriz final

distribuir_vector_matriz(
  vector = paste0(book$FA, book$FB),
  niveles_FA = length(levels(book$FA)),
  niveles_FB = length(levels(book$FB)),
  num_bloques = length(levels(book$block)))
      [,1]   [,2]   [,3]  
 [1,] "A3B1" "A1B1" "A2B1"
 [2,] "A3B2" "A1B2" "A2B2"
 [3,] "A2B2" "A1B2" "A3B2"
 [4,] "A2B1" "A1B1" "A3B1"
 [5,] "A1B2" "A2B2" "A3B2"
 [6,] "A1B1" "A2B1" "A3B1"
 [7,] "A1B1" "A3B1" "A2B1"
 [8,] "A1B2" "A3B2" "A2B2"
 [9,] "A3B2" "A2B2" "A1B2"
[10,] "A3B1" "A2B1" "A1B1"
[11,] "A3B1" "A1B1" "A2B1"
[12,] "A3B2" "A1B2" "A2B2"
niveles_FA <- length(levels(book$FA))
niveles_FB <- length(levels(book$FB))
niveles_col <- niveles_FA

generar_vector <- function(niveles_FB, niveles_FA, repeticiones) {
  vector_FB <- rep(1:niveles_FB, niveles_FA)
  vector_final <- vector_FB
  
  for (i in 2:repeticiones) {
    vector_FB <- vector_FB + niveles_FB
    vector_final <- c(vector_final, vector_FB)
  }
  
  return(vector_final)
}

bookst <- data.frame(plots = book$plots,
                     block = as.factor(book$block),
                     FA = as.factor(book$FA),
                     FB = as.factor(book$FB),
                     row = rev(generar_vector(niveles_FA = 3,
                         niveles_FB = 2,
                         repeticiones = 6)),
                     col = as.factor(as.integer(rep(1:niveles_FA,
                                            each = niveles_FB))))
bookst %>% 
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)

Guardar el libro generado

write.table(salida$book,
            "books/rcbdstplot.txt",
            row.names = FALSE,
            sep = "\t")

write.xlsx(salida$book,
           "books/rcbdstplot.xlsx",
           sheetName = "book",
           append = FALSE,
           row.names = FALSE)

Guardar el libro de campo generado

write.table(salida %>% zigzag(),
            "books/rcbdstplot.txt",
            row.names = FALSE,
            sep = "\t")

write.xlsx(salida %>% zigzag(),
           "books/rcbdstplot.xlsx",
           sheetName = "book",
           append = FALSE,
           row.names = FALSE)
# Esta forma no es la adecuada

agricolaeplotr::plot_strip(design = salida,
                           factor_name_1 = "FA",
                           factor_name_2 = "FB")
ggplot(bookst,
       aes(col, y = row)) +
  geom_tile(aes(fill = FA)) + 
  theme_bw() + 
  theme(line = element_blank()) + 
  geom_text(aes(label = plots), colour = "black")
ggplot(bookst,
       aes(col, y = row)) +
  geom_tile(aes(fill = FB)) + 
  theme_bw() + 
  theme(line = element_blank()) + 
  geom_text(aes(label = plots), colour = "black")

En forma de horientación horizontal

distribuir_vector_matriz <- function(vector, niveles_FA, niveles_FB, num_bloques) {
  # Verificar que el número de niveles de FB sea menor o igual a la mitad del número de bloques
  stopifnot(niveles_FB <= num_bloques/2)
  
  # Calcular el número de columnas por bloque
  columnas_bloque <- niveles_FA
  
  # Calcular el número de filas por bloque
  filas_bloque <- niveles_FB
  
  # Calcular el número total de filas
  num_filas <- filas_bloque
  
  # Calcular el número total de filas
  num_columnas <- columnas_bloque * num_bloques
  
  # Calcular el número de bloques completos
  num_bloques_completos <- num_filas %/% filas_bloque
  
  # Crear una matriz vacía
  matriz <- matrix(NA, nrow = num_filas, ncol = num_columnas)
  
  # Distribuir los valores en la matriz
  for (i in 1:num_bloques_completos) {
    inicio_fila <- (i - 1) * filas_bloque + 1
    fin_fila <- i * filas_bloque
    inicio_vector <- (i - 1) * columnas_bloque * filas_bloque + 1
    fin_vector <- i * columnas_bloque * filas_bloque
    matriz[inicio_fila:fin_fila, ] <- matrix(vector[inicio_vector:fin_vector], nrow = filas_bloque, byrow = TRUE) %>% t()
  }
  
  # Manejar los bloques incompletos
  if (num_filas %% filas_bloque != 0) {
    inicio_fila <- num_bloques_completos * filas_bloque + 1
    fin_fila <- num_filas
    inicio_vector <- num_bloques_completos * columnas_bloque * filas_bloque + 1
    fin_vector <- length(vector)
    matriz[inicio_fila:fin_fila, ] <- matrix(vector[inicio_vector:fin_vector], nrow = fin_fila - inicio_fila + 1, byrow = TRUE)
  }
  
  return(matriz)
}
distribuir_vector_matriz(
  vector = book$FA,
  niveles_FA = length(levels(book$FA)),
  niveles_FB = length(levels(book$FB)),
  num_bloques = length(levels(book$block)))
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] "A3" "A1" "A2" "A3" "A1" "A2" "A3" "A1" "A2" "A3"  "A1"  "A2"  "A3"  "A1" 
[2,] "A3" "A1" "A2" "A3" "A1" "A2" "A3" "A1" "A2" "A3"  "A1"  "A2"  "A3"  "A1" 
     [,15] [,16] [,17] [,18]
[1,] "A2"  "A3"  "A1"  "A2" 
[2,] "A2"  "A3"  "A1"  "A2" 

Sketch del diseño para FB

distribuir_vector_matriz(
  vector = book$FB,
  niveles_FA = length(levels(book$FA)),
  niveles_FB = length(levels(book$FB)),
  num_bloques = length(levels(book$block)))
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,] "B1" "B1" "B1" "B1" "B1" "B1" "B1" "B1" "B1" "B1"  "B1"  "B1"  "B1"  "B1" 
[2,] "B2" "B2" "B2" "B2" "B2" "B2" "B2" "B2" "B2" "B2"  "B2"  "B2"  "B2"  "B2" 
     [,15] [,16] [,17] [,18]
[1,] "B1"  "B1"  "B1"  "B1" 
[2,] "B2"  "B2"  "B2"  "B2" 

Matriz final

distribuir_vector_matriz(
  vector = paste0(book$FA, book$FB),
  niveles_FA = length(levels(book$FA)),
  niveles_FB = length(levels(book$FB)),
  num_bloques = length(levels(book$block)))
     [,1]   [,2]   [,3]   [,4]   [,5]   [,6]   [,7]   [,8]   [,9]   [,10] 
[1,] "A3B1" "A1B1" "A2B1" "A3B1" "A1B1" "A2B1" "A3B1" "A1B1" "A2B1" "A3B1"
[2,] "A3B2" "A1B2" "A2B2" "A3B2" "A1B2" "A2B2" "A3B2" "A1B2" "A2B2" "A3B2"
     [,11]  [,12]  [,13]  [,14]  [,15]  [,16]  [,17]  [,18] 
[1,] "A1B1" "A2B1" "A3B1" "A1B1" "A2B1" "A3B1" "A1B1" "A2B1"
[2,] "A1B2" "A2B2" "A3B2" "A1B2" "A2B2" "A3B2" "A1B2" "A2B2"
niveles_FA <- length(levels(book$FA))
niveles_FB <- length(levels(book$FB))
niveles_col <- niveles_FA * r

bookst <- data.frame(plots = book$plots,
                     block = as.factor(book$block),
                     FA = as.factor(book$FA),
                     FB = as.factor(book$FB),
                     col = as.factor(as.integer(rep(1:niveles_col,
                                                    each = niveles_FB))),
                     row = rev(as.factor(as.integer(rep(1:niveles_FB)))))
bookst %>% 
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)

Guardar el libro generado

write.table(salida$book,
            "books/rcbdstplot.txt",
            row.names = FALSE,
            sep = "\t")

write.xlsx(salida$book,
           "books/rcbdstplot.xlsx",
           sheetName = "book",
           append = FALSE,
           row.names = FALSE)

Guardar el libro de campo generado

write.table(salida %>% zigzag(),
            "books/rcbdstplot.txt",
            row.names = FALSE,
            sep = "\t")

write.xlsx(salida %>% zigzag(),
           "books/rcbdstplot.xlsx",
           sheetName = "book",
           append = FALSE,
           row.names = FALSE)
# Esta forma no es la adecuada

agricolaeplotr::plot_strip(design = salida,
                           factor_name_1 = "FA",
                           factor_name_2 = "FB")
ggplot(bookst,
       aes(col, y = row)) +
  geom_tile(aes(fill = FA)) + 
  theme_bw() + 
  theme(line = element_blank()) + 
  geom_text(aes(label = plots), colour = "black")
ggplot(bookst,
       aes(col, y = row)) +
  geom_tile(aes(fill = FB)) + 
  theme_bw() + 
  theme(line = element_blank()) + 
  geom_text(aes(label = plots), colour = "black")

Crear un libro de campo con el paquete edibble


menu_strip()
design("Strip-Plot Design | Strip-Unit Design") %>%
  set_units(block = 4,
            row = nested_in(block, 5),
            col = nested_in(block, 3),
            unit = nested_in(block, crossed_by(row, col))) %>%
  set_trts(trt1 = 5,
           trt2 = 3) %>%
  allot_trts(trt1 ~ row,
             trt2 ~ col) %>%
  assign_trts("random", seed = 411) %>%
  serve_table()
rcbd <- takeout(menu_strip(t1 = 3,
                           t2 = 2,
                           r = 6,
                           seed = 123))
rcbd %>% 
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)
rcbd2 <- design("Strip-Plot Design | Strip-Unit Design") %>%
  set_units(block = 6,
            row = nested_in(block, 2),
            col = nested_in(block, 3),
            unit = nested_in(block, crossed_by(row, col))) %>%
  set_trts(trt1 = FA,
           trt2 = FB) %>%
  allot_trts(trt1 ~ col,
             trt2 ~ row) %>%
  assign_trts("random", seed = 123) %>%
  serve_table()
rcbd2 %>% 
  gt::gt() %>%
  gt::opt_interactive(use_search = TRUE,
                      use_filters = TRUE,
                      use_compact_mode = TRUE,
                      page_size_default = 5)
write.table(rcbd2 %>% as.data.frame(),
            "books/rcbdstplot.txt",
            row.names = FALSE,
            sep = "\t")

write.xlsx(rcbd2 %>% as.data.frame(),
           "books/rcbdstplot.xlsx",
           sheetName = "book",
           append = FALSE,
           row.names = FALSE)
deggust::autoplot(rcbd2)
plot(rcbd2)

Análisis de DBCA en arreglo factorial de bloques divididos


Importación de datos


archivos <- list.files(pattern = "datos strip plot.xlsx", 
                       full.names = TRUE,
                       recursive = TRUE)

# Importación
data <- readxl::read_xlsx(archivos,
                           sheet = "ej1")

# Preprocesamiento

data <- data %>%
  mutate_if(is.character, factor) %>%
  mutate(bloque = factor(bloque),
         trat = factor(trat),
         aplic = factor(aplic))
attach(data)

Creación del modelo lineal


modelo.dbca1 <- lm(rdto ~ trat * aplic + bloque/trat + bloque/aplic + bloque, data = data)
modelo.dbca2 <- lm(rdto ~ trat + aplic + bloque/trat + bloque/aplic + bloque, data = data)
broom::glance(modelo.dbca1) %>%
  bind_rows(broom::glance(modelo.dbca2)) %>%
  dplyr::mutate(Modelo = c("A * B + bloque + bloque/A + bloque/B",
                           "A + B + bloque + bloque/A + bloque/B")) %>%
  dplyr::select(Modelo, AIC, BIC) %>%
  dplyr::arrange(BIC) %>%
  dplyr::mutate(Mérito = 1:n()) %>%
  dplyr::relocate(Mérito, Modelo) %>%
  gt()
Mérito Modelo AIC BIC
1 A * B + bloque + bloque/A + bloque/B 71.81655 94.19958
2 A + B + bloque + bloque/A + bloque/B 85.83288 101.14758

Definición del modelo


modelo.dbca <- lm(rdto ~ trat * aplic + bloque/trat + bloque/aplic + bloque, data = data)
summary(modelo.dbca)

Call:
lm(formula = rdto ~ trat * aplic + bloque/trat + bloque/aplic + 
    bloque, data = data)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.0417 -0.2292  0.0000  0.2292  1.0417 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)     9.208e+00  8.478e-01  10.862 3.61e-05 ***
trat2          -2.250e+00  1.094e+00  -2.056  0.08556 .  
trat3          -1.375e+00  1.094e+00  -1.256  0.25571    
aplic2          4.500e+00  1.130e+00   3.981  0.00728 ** 
aplic3         -3.333e+00  1.130e+00  -2.949  0.02565 *  
aplic4         -5.000e+00  1.130e+00  -4.423  0.00446 ** 
bloque2        -1.417e+00  9.789e-01  -1.447  0.19801    
trat2:aplic2    2.000e+00  1.384e+00   1.445  0.19868    
trat3:aplic2   -5.000e-01  1.384e+00  -0.361  0.73036    
trat2:aplic3    1.000e+00  1.384e+00   0.722  0.49728    
trat3:aplic3   -2.584e-15  1.384e+00   0.000  1.00000    
trat2:aplic4    3.000e+00  1.384e+00   2.167  0.07337 .  
trat3:aplic4    3.000e+00  1.384e+00   2.167  0.07337 .  
trat2:bloque2   1.500e+00  9.789e-01   1.532  0.17634    
trat3:bloque2   7.500e-01  9.789e-01   0.766  0.47265    
aplic2:bloque2  3.000e+00  1.130e+00   2.654  0.03783 *  
aplic3:bloque2  3.667e+00  1.130e+00   3.244  0.01760 *  
aplic4:bloque2 -1.000e+00  1.130e+00  -0.885  0.41039    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.9789 on 6 degrees of freedom
Multiple R-squared:  0.9847,    Adjusted R-squared:  0.9415 
F-statistic: 22.76 on 17 and 6 DF,  p-value: 0.0004614

Verificación visual de los supuestos del modelo


performance::check_model(modelo.dbca)
ggResidpanel::resid_panel(modelo.dbca)
influence.measures(modelo.dbca)
Influence measures of
     lm(formula = rdto ~ trat * aplic + bloque/trat + bloque/aplic +      bloque, data = data) :

    dfb.1_  dfb.trt2  dfb.trt3  dfb.apl2  dfb.apl3  dfb.apl4 dfb.blq2
1   0.0451 -5.24e-02 -5.24e-02  6.37e-17  2.71e-01  1.83e-16  -0.0781
2  -0.6834  4.41e-01  4.41e-01  4.56e-01  4.56e-01  4.56e-01   0.3945
3  -0.0759  8.82e-02  8.82e-02 -4.32e-17 -7.59e-17 -4.56e-01   0.1315
4   0.1079 -1.25e-01 -1.25e-01  6.48e-01  4.00e-17  7.72e-17  -0.1869
5   0.1314 -3.05e-01  6.37e-16  4.64e-16 -3.94e-01  6.10e-16  -0.2276
6   0.0224  8.69e-02 -6.06e-18 -2.24e-02 -2.24e-02 -2.24e-02  -0.0389
7  -0.3775  8.77e-01 -1.25e-15 -6.36e-16 -1.51e-15  1.13e+00   0.6539
8   0.0890 -2.07e-01  3.21e-17 -2.67e-01  2.48e-16 -3.13e-17  -0.1542
9  -0.0987 -4.41e-17  2.29e-01 -1.40e-16  2.96e-01 -5.48e-16   0.1710
10  0.0906  5.40e-17  3.51e-01 -9.06e-02 -9.06e-02 -9.06e-02  -0.1569
11  0.2080 -6.97e-16 -4.83e-01 -7.43e-16 -8.31e-16 -6.24e-01  -0.3603
12 -0.0302  3.37e-17  7.02e-02  9.06e-02  8.40e-18 -7.30e-17   0.0523
13  0.1079 -1.25e-01 -1.25e-01 -3.24e-01 -1.03e-16 -1.39e-16  -0.1869
14  0.0451 -5.24e-02 -5.24e-02  7.97e-17 -1.35e-01 -1.04e-19  -0.0781
15 -0.0759  8.82e-02  8.82e-02 -1.38e-16 -3.79e-17  2.28e-01   0.1315
16  0.2278 -2.65e-01 -2.65e-01 -2.28e-01 -2.28e-01 -2.28e-01   0.3945
17 -0.0302  6.75e-17  7.02e-02  9.06e-02  5.85e-17 -2.53e-17   0.0523
18 -0.0987 -2.21e-17  2.29e-01 -1.05e-16  2.96e-01 -1.72e-16   0.1710
19  0.2080 -4.65e-17 -4.83e-01  1.37e-16 -1.04e-16 -6.24e-01  -0.3603
20  0.0906 -6.75e-17 -2.11e-01 -9.06e-02 -9.06e-02 -9.06e-02  -0.1569
21  0.0890 -2.07e-01  5.08e-17 -2.67e-01  1.79e-16 -1.68e-17  -0.1542
22  0.1314 -3.05e-01 -3.25e-16  2.79e-16 -3.94e-01 -2.38e-16  -0.2276
23 -0.3775  8.77e-01 -2.33e-15 -6.23e-16 -1.60e-15  1.13e+00   0.6539
24  0.0224 -5.22e-02  2.48e-17 -2.24e-02 -2.24e-02 -2.24e-02  -0.0389
   dfb.trt2.p2 dfb.trt3.p2  dfb.t2.3  dfb.t3.3  dfb.t2.4  dfb.t3.4 dfb.trt2.b2
1    -1.74e-17   -5.31e-17 -1.66e-01 -1.66e-01 -7.83e-17 -1.06e-16    1.17e-01
2    -2.79e-01   -2.79e-01 -2.79e-01 -2.79e-01 -2.79e-01 -2.79e-01   -1.97e-01
3    -2.11e-17    4.89e-17  9.67e-17  9.48e-17  2.79e-01  2.79e-01   -1.97e-01
4    -3.97e-01   -3.97e-01 -4.71e-17  6.66e-17 -1.44e-16 -8.25e-17    2.80e-01
5    -2.14e-16   -5.36e-16 -9.66e-01 -7.26e-16 -2.16e-16 -3.79e-16    6.83e-01
6    -5.50e-02    7.95e-18 -5.50e-02  1.00e-17 -5.50e-02 -2.36e-18   -3.89e-02
7     1.16e-15    1.26e-15  1.72e-15  1.16e-15  2.77e+00  1.25e-15   -1.96e+00
8    -6.54e-01   -3.81e-18 -2.23e-16 -1.45e-16 -3.72e-17  6.56e-17    4.63e-01
9     7.71e-17    1.40e-16  3.84e-16  7.25e-01  3.66e-16  3.34e-16   -1.48e-16
10    0.00e+00   -2.22e-01 -2.61e-17 -2.22e-01  1.36e-16 -2.22e-01    0.00e+00
11    5.62e-16    2.71e-16  9.49e-16  5.20e-16  2.08e-16 -1.53e+00   -4.16e-16
12    1.23e-17    2.22e-01 -1.79e-17 -6.91e-17  4.71e-17  2.78e-17   -1.51e-17
13    3.97e-01    3.97e-01 -2.67e-17  2.96e-17  4.00e-17  5.92e-17    2.80e-01
14   -3.54e-17    2.12e-17  1.66e-01  1.66e-01  1.58e-17  3.80e-17    1.17e-01
15    2.13e-16    1.76e-16  1.25e-16  1.52e-16 -2.79e-01 -2.79e-01   -1.97e-01
16    2.79e-01    2.79e-01  2.79e-01  2.79e-01  2.79e-01  2.79e-01   -1.97e-01
17    0.00e+00   -2.22e-01 -5.41e-17 -8.40e-17 -1.41e-17 -3.22e-17   -4.53e-17
18    1.89e-16   -4.65e-17  2.14e-16 -7.25e-01  1.38e-16  8.10e-17   -1.97e-16
19   -1.23e-16   -1.61e-16 -2.15e-16  1.04e-16 -6.24e-16  1.53e+00    1.04e-16
20   -4.93e-17    2.22e-01 -1.31e-17  2.22e-01 -4.53e-17  2.22e-01    6.04e-17
21    6.54e-01   -1.19e-16 -2.49e-16 -2.17e-16 -5.83e-18  1.15e-17    4.63e-01
22   -1.99e-16    1.38e-16  9.66e-01  1.02e-16  3.86e-16  4.89e-16    6.83e-01
23    1.46e-15    1.74e-15  2.19e-15  1.76e-15 -2.77e+00  2.46e-15   -1.96e+00
24    5.50e-02   -1.44e-17  5.50e-02 -1.39e-17  5.50e-02 -1.29e-17   -3.89e-02
   dfb.trt3.b2  dfb.a2.2  dfb.a3.2  dfb.a4.2  dffit    cov.r  cook.d  hat inf
1     1.17e-01 -5.31e-17 -1.35e-01 -1.17e-16  0.406 8.75e+01 0.01087 0.75   *
2    -1.97e-01 -2.28e-01 -2.28e-01 -2.28e-01 -0.683 6.13e+01 0.03019 0.75   *
3    -1.97e-01 -1.94e-17  7.59e-17  2.28e-01 -0.683 6.13e+01 0.03019 0.75   *
4     2.80e-01 -3.24e-01 -4.64e-17  4.20e-17  0.971 3.55e+01 0.05918 0.75   *
5    -9.48e-17 -4.02e-16  7.89e-01 -4.53e-16 -2.366 3.54e-01 0.27174 0.75    
6    -1.27e-17  4.49e-02  4.49e-02  4.49e-02  0.135 1.04e+02 0.00121 0.75   *
7    -1.09e-16 -6.75e-16  3.77e-16 -2.27e+00  6.796 1.09e-09 0.75483 0.75   *
8     4.17e-17  5.34e-01 -1.14e-16 -5.00e-17 -1.602 6.20e+00 0.14614 0.75    
9    -5.13e-01  0.00e+00 -5.92e-01  2.83e-16  1.777 3.42e+00 0.17391 0.75    
10   -1.57e-01  1.81e-01  1.81e-01  1.81e-01  0.544 7.50e+01 0.01932 0.75   *
11    1.08e+00  3.84e-16  4.16e-16  1.25e+00 -3.744 7.39e-04 0.48309 0.75   *
12   -1.57e-01 -1.81e-01  6.48e-17  6.92e-17  0.544 7.50e+01 0.01932 0.75   *
13    2.80e-01 -3.24e-01  5.68e-17  1.14e-16 -0.971 3.55e+01 0.05918 0.75   *
14    1.17e-01 -6.91e-17 -1.35e-01 -4.36e-17 -0.406 8.75e+01 0.01087 0.75   *
15   -1.97e-01 -7.41e-18 -7.59e-17  2.28e-01  0.683 6.13e+01 0.03019 0.75   *
16   -1.97e-01 -2.28e-01 -2.28e-01 -2.28e-01  0.683 6.13e+01 0.03019 0.75   *
17   -1.57e-01 -1.81e-01  1.56e-17  6.14e-17 -0.544 7.50e+01 0.01932 0.75   *
18   -5.13e-01  2.33e-17 -5.92e-01  1.46e-18 -1.777 3.42e+00 0.17391 0.75    
19    1.08e+00  4.06e-17  4.16e-16  1.25e+00  3.744 7.39e-04 0.48309 0.75   *
20   -1.57e-01  1.81e-01  1.81e-01  1.81e-01 -0.544 7.50e+01 0.01932 0.75   *
21    9.31e-17  5.34e-01 -2.63e-17 -5.27e-17  1.602 6.20e+00 0.14614 0.75    
22    2.65e-16 -2.48e-16  7.89e-01 -3.05e-16  2.366 3.54e-01 0.27174 0.75    
23    8.17e-16 -1.23e-15 -7.54e-16 -2.27e+00 -6.796 1.09e-09 0.75483 0.75   *
24   -3.10e-17  4.49e-02  4.49e-02  4.49e-02 -0.135 1.04e+02 0.00121 0.75   *
influenceIndexPlot(modelo.dbca)

Cumplimiento de supuestos del modelo lineal general


Independencia de residuos

\(H_0: \text{Los residuos del rendimiento son completamente aleatorios e independientes}\)

\(H_1: \text{Los residuos del rendimiento no son completamente aleatorios e independientes}\)

durbinWatsonTest(modelo.dbca,
                 reps = 5000,
                 max.lag = 5)
 lag Autocorrelation D-W Statistic p-value
   1     -0.34933575      2.695652  0.2784
   2     -0.14673913      2.094203  0.9692
   3      0.34812802      1.028986  0.1456
   4     -0.52053140      2.714976  0.1972
   5      0.07880435      1.443539  0.9180
 Alternative hypothesis: rho[lag] != 0
dwtest(modelo.dbca, alternative = "two.sided")

    Durbin-Watson test

data:  modelo.dbca
DW = 2.6957, p-value = 0.278
alternative hypothesis: true autocorrelation is not 0

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los residuos del rendimiento son completamente aleatorios e independientes.

Normalidad de residuos

\(H_0: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

\(H_1: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)

shapiro.test(rstudent(modelo.dbca))

    Shapiro-Wilk normality test

data:  rstudent(modelo.dbca)
W = 0.92973, p-value = 0.09615
ad.test(rstudent(modelo.dbca))

    Anderson-Darling normality test

data:  rstudent(modelo.dbca)
A = 0.73842, p-value = 0.04692
lillie.test(rstudent(modelo.dbca))

    Lilliefors (Kolmogorov-Smirnov) normality test

data:  rstudent(modelo.dbca)
D = 0.14393, p-value = 0.2231
ks.test(rstudent(modelo.dbca), "pnorm",
        alternative = "two.sided",
        exact = T,
        simulate.p.value = T,
        B = 10000)

    Exact one-sample Kolmogorov-Smirnov test

data:  rstudent(modelo.dbca)
D = 0.096589, p-value = 0.9627
alternative hypothesis: two-sided
cvm.test(rstudent(modelo.dbca))

    Cramer-von Mises normality test

data:  rstudent(modelo.dbca)
W = 0.12618, p-value = 0.04565
pearson.test(rstudent(modelo.dbca))

    Pearson chi-square normality test

data:  rstudent(modelo.dbca)
P = 8, p-value = 0.1562
sf.test(rstudent(modelo.dbca))

    Shapiro-Francia normality test

data:  rstudent(modelo.dbca)
W = 0.90414, p-value = 0.02824

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la distribución de los residuos del rendimiento es similar a la función normal o gaussiana.

Homocedasticidad

\(H_0\): La varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento

\(H_1\): La varianza del rendimiento no es constante con respecto a los valores ajustados del rendimiento

ncvTest(modelo.dbca)
Non-constant Variance Score Test 
Variance formula: ~ fitted.values 
Chisquare = 2.73003, Df = 1, p = 0.098477
bptest(modelo.dbca)

    studentized Breusch-Pagan test

data:  modelo.dbca
BP = 24, df = 17, p-value = 0.1194
bptest(modelo.dbca, studentize = F)

    Breusch-Pagan test

data:  modelo.dbca
BP = 21.652, df = 17, p-value = 0.1985
olsrr::ols_test_breusch_pagan(modelo.dbca)

 Breusch Pagan Test for Heteroskedasticity
 -----------------------------------------
 Ho: the variance is constant            
 Ha: the variance is not constant        

              Data               
 --------------------------------
 Response : rdto 
 Variables: fitted values of rdto 

        Test Summary          
 -----------------------------
 DF            =    1 
 Chi2          =    2.73003 
 Prob > Chi2   =    0.09847741 

Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento.

Recomendación. Debido a que se cumple con el supuesto de homocedasticidad, para evaluar los efectos de los tratamientos con respecto al rendimiento, se debe proceder a realizar el análisis de varianza.

Estadísticas globales

modelo.dbca %>% gvlma()

Call:
lm(formula = rdto ~ trat * aplic + bloque/trat + bloque/aplic + 
    bloque, data = data)

Coefficients:
   (Intercept)           trat2           trat3          aplic2          aplic3  
     9.208e+00      -2.250e+00      -1.375e+00       4.500e+00      -3.333e+00  
        aplic4         bloque2    trat2:aplic2    trat3:aplic2    trat2:aplic3  
    -5.000e+00      -1.417e+00       2.000e+00      -5.000e-01       1.000e+00  
  trat3:aplic3    trat2:aplic4    trat3:aplic4   trat2:bloque2   trat3:bloque2  
    -2.584e-15       3.000e+00       3.000e+00       1.500e+00       7.500e-01  
aplic2:bloque2  aplic3:bloque2  aplic4:bloque2  
     3.000e+00       3.667e+00      -1.000e+00  


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = .) 

                       Value p-value                   Decision
Global Stat        5.146e+00 0.27259    Assumptions acceptable.
Skewness           1.021e-31 1.00000    Assumptions acceptable.
Kurtosis           3.828e-02 0.84488    Assumptions acceptable.
Link Function      4.376e+00 0.03645 Assumptions NOT satisfied!
Heteroscedasticity 7.324e-01 0.39210    Assumptions acceptable.

Análisis de varianza

\[Y_{ijk} = \mu + \gamma_{k} + \tau_{i} + \text{Error}(\tau\gamma)_{ik} + \beta_{j} + \text{Error}(\beta\gamma)_{jk} + (\tau\beta)_{ij} + \epsilon_{ijk}\]

\[\hat{Y}_{ijk} = \mu + \gamma_{k} + \tau_{i} + \text{Error}(\tau\gamma)_{ik} + \beta_{j} + \text{Error}(\beta\gamma)_{jk} + (\tau\beta)_{ij} \]

Dónde:

\(Y_{ijk}\) = Valor observado de la variable respuesta.

\(\hat{Y}_{ijk}\) = Valor ajustado de la variable respuesta.

\(\mu\) = Promedio observado de la variable respuesta.

\(\tau_{i}\) = Efecto del i-ésimo nivel del factor A.

\(\beta_{j}\) = Efecto del j-ésimo nivel del factor B.

\(\gamma_{k}\) = Efecto del k-ésimo nivel del factor Bloque.

\((\tau\gamma)_{ik}\) = Residuo observado del modelo a nivel de las columnas.

\(\text{Error}(\beta\gamma)_{jk}\) = Residuo observado del modelo a nivel de las filas.

\(\text{Error}(\tau\beta)_{ij}\) = Efecto de la interacción entre el i-ésimo nivel del factor A y el j-ésimo nivel del factor B.

\(\epsilon_{ijk}\) = Residuo observado del modelo a nivel de subsubparcelas.

Pruebas de hipótesis

Para el factor A (tratamiento):

\(H_0: \tau_{A1} = \tau_{A2} = \tau_{A3} = 0\)

\(H_1: \text{En al menos un nivel del factor A el } \tau \text{ es diferente a los demás.}\)

\(H_1: \tau_i \neq 0\text{; en al menos un nivel del factor A.}\)

Para el factor B (aplicación):

\(H_0: \beta_{B1} = \beta_{B2} = \beta_{B3} = \beta_{B4} = 0\)

\(H_1: \text{En al menos un nivel del factor B el } \beta \text{ es diferente a los demás.}\)

\(H_1: \beta_j \neq 0\text{; en al menos un nivel del factor B.}\)

Para la interacción entre factor A y factor B:

\(H_0: (\tau\beta)_{A1B1} = (\tau\beta)_{A1B2} = (\tau\beta)_{A1B3} = (\tau\beta)_{A1B4} = (\tau\beta)_{A2B1} = (\tau\beta)_{A2B2} = ... = (\tau\beta)_{A3B4} = 0\)

\(H_1: \text{En al menos una interacción entre el factor A y el factor B el } (\tau\beta) \text{ es diferente a los demás.}\)

\(H_1: (\tau\beta)_{ij} \neq 0\text{; en al menos una interacción entre el factor A y el factor B.}\)

Precaución

  • Si se ignora el diseño experimental, se obtienen los siguientes resultados, incorrectos. Observe que los grados de libertad del error es mayor, lo que facilita la detección de diferencias que en realidad no existen.
anova(modelo.dbca, test = "F")
Analysis of Variance Table

Response: rdto
             Df Sum Sq Mean Sq  F value   Pr(>F)    
trat          2   0.75   0.375   0.3913  0.69225    
aplic         3 330.12 110.042 114.8261 1.09e-05 ***
bloque        1   3.37   3.375   3.5217  0.10967    
trat:aplic    6  11.25   1.875   1.9565  0.21719    
trat:bloque   2   2.25   1.125   1.1739  0.37131    
aplic:bloque  3  23.12   7.708   8.0435  0.01593 *  
Residuals     6   5.75   0.958                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Importante

Necesitamos especificar correctamente el término de error para el factor A. Debe tenerse en cuenta que la forma del Error es “Error(bloque:A)” en el caso de efectos aleatorios o “Error(bloque/A)” para el caso de efectos fijos y puede cambiar dependiendo de la disposición de los datos. La clave es conocer los grados de libertad correcto para saber que se obtienen los resultados correctos. En el factor B se trabaja con “Error(bloque:B)” en el caso de efectos aleatorios o “Error(bloque/B)” para el caso de efectos fijos. Para la interacción se trabaja con “Error(bloque/A/B)” para el caso de efectos fijos o con “Error(bloque:A:B)” en el caso de efectos aleatorios.

aov(rdto ~ bloque + trat * aplic +
      Error(bloque/trat+bloque/aplic), data = data) -> aov.dbca
summary(aov.dbca)

Error: bloque
       Df Sum Sq Mean Sq
bloque  1  3.375   3.375

Error: bloque:trat
          Df Sum Sq Mean Sq F value Pr(>F)
trat       2   0.75   0.375   0.333   0.75
Residuals  2   2.25   1.125               

Error: bloque:aplic
          Df Sum Sq Mean Sq F value Pr(>F)  
aplic      3  330.1  110.04   14.28 0.0279 *
Residuals  3   23.1    7.71                 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Error: Within
           Df Sum Sq Mean Sq F value Pr(>F)
trat:aplic  6  11.25  1.8750   1.957  0.217
Residuals   6   5.75  0.9583               
data %>% with(agricolae::strip.plot(BLOCK = bloque,
                                    COL = trat,
                                    ROW = aplic,
                                    Y = rdto))

ANALYSIS STRIP PLOT:  rdto 
Class level information

trat    :  1 2 3 
aplic   :  3 1 4 2 
bloque  :  1 2 

Number of observations:  24 

model Y: rdto ~ bloque + trat + Ea + aplic + Eb + aplic:trat + Ec 

Analysis of Variance Table

Response: rdto
           Df Sum Sq Mean Sq F value  Pr(>F)  
bloque      1   3.37   3.375                  
trat        2   0.75   0.375  0.3333 0.75000  
Ea          2   2.25   1.125                  
aplic       3 330.13 110.042 14.2757 0.02787 *
Eb          3  23.12   7.708                  
aplic:trat  6  11.25   1.875  1.9565 0.21719  
Ec          6   5.75   0.958                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

cv(a) = 13.1 %, cv(b) = 34.2 %, cv(c) = 12 %, Mean = 8.125 
broom::tidy(aov.dbca)
# A tibble: 7 × 7
  stratum      term          df   sumsq  meansq statistic p.value
  <chr>        <chr>      <dbl>   <dbl>   <dbl>     <dbl>   <dbl>
1 bloque       bloque         1   3.37    3.37     NA     NA     
2 bloque:trat  trat           2   0.750   0.375     0.333  0.75  
3 bloque:trat  Residuals      2   2.25    1.13     NA     NA     
4 bloque:aplic aplic          3 330.    110.       14.3    0.0279
5 bloque:aplic Residuals      3  23.1     7.71     NA     NA     
6 Within       trat:aplic     6  11.3     1.88      1.96   0.217 
7 Within       Residuals      6   5.75    0.958    NA     NA     

Valor de la tabla de F para el factor A con una significancia de 0.05.

qf(0.95, 2, 2)
[1] 19

Valor de la tabla de F para el factor B con una significancia de 0.05.

qf(0.95, 3, 3)
[1] 9.276628

Valor de la tabla de F para la interacción A:B con una significancia de 0.05.

qf(0.95, 6, 6)
[1] 4.283866

Conclusión.

Con respecto al Factor A: A un nivel de significancia de 0.05, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los niveles del factor A tiene un efecto estadísticamente similar de 0.

Con respecto al Factor B: A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos un nivel del factor B tiene un efecto estadísticamente distinto de 0.

Con respecto a la interacción entre el Factor A y Factor B: A un nivel de significancia de 0.05, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, no existió un efecto de antagonismo o sinergismo en alguna interacción dada por los niveles de A y de B.

get_dfe_stplot <- function(object, name_factor) {
  library(broom)
  tidy_aov <- broom::tidy(object)
  df_rep_A_residuals <- tidy_aov %>% 
    dplyr::filter(endsWith(stratum, paste0(":",name_factor)) & 
                    term == "Residuals") %>%
    dplyr::pull(df)
  return(df_rep_A_residuals)
}
get_dfe_stplot(aov.dbca, "trat")
[1] 2
get_mse_stplot <- function(object, name_factor) {
  library(broom)
  tidy_aov <- broom::tidy(object)
  meansq_rep_A_residuals <- tidy_aov %>% 
    dplyr::filter(endsWith(stratum, paste0(":",name_factor)) & 
                    term == "Residuals") %>%
    dplyr::pull(meansq)
  return(meansq_rep_A_residuals)
}
get_mse_stplot(aov.dbca, "trat")
[1] 1.125
get_dfe_stplot(aov.dbca, "aplic")
[1] 3
get_mse_stplot(aov.dbca, "aplic")
[1] 7.708333
agricolae::cv.model(modelo.dbca)
[1] 12.04855
cv.a <- sqrt(get_mse_stplot(aov.dbca, "trat"))*100/mean(data$rdto)
cv.a
[1] 13.05428
cv.b <- sqrt(get_mse_stplot(aov.dbca, "aplic"))*100/mean(data$rdto)
cv.b
[1] 34.17094
cv.c <- sqrt(dvmisc::get_mse(modelo.dbca))*100/mean(data$rdto)
cv.c
[1] 12.04855

Comparaciones de medias para los efectos principales del Factor A

data %>% with(LSD.test(
  rdto, # Cambiar según nombre de variable respuesta
  trat, # Cambiar según nombre de variable independiente
  DFerror = get_dfe_stplot(aov.dbca, "trat"), 
  MSerror = get_mse_stplot(aov.dbca, "trat"),
  alpha = 0.05,
  group=TRUE,
  main = NULL,
  console=TRUE))

Study: rdto ~ trat

LSD t Test for rdto 

Mean Square Error:  1.125 

trat,  means and individual ( 95 %) CI

   rdto      std r      LCL      UCL Min Max
1 8.250 4.496030 8 6.636505 9.863495   2  15
2 8.250 4.682795 8 6.636505 9.863495   3  17
3 7.875 3.399054 8 6.261505 9.488495   5  14

Alpha: 0.05 ; DF Error: 2
Critical Value of t: 4.302653 

least Significant Difference: 2.281826 

Treatments with the same letter are not significantly different.

   rdto groups
1 8.250      a
2 8.250      a
3 7.875      a

Comparaciones de medias para los efectos principales del Factor B

data %>% with(LSD.test(
  rdto, # Cambiar según nombre de variable respuesta
  aplic, # Cambiar según nombre de variable independiente
  DFerror = get_dfe_stplot(aov.dbca, "aplic"), 
  MSerror = get_mse_stplot(aov.dbca, "aplic"),
  alpha = 0.05,
  group = TRUE,
  main = NULL,
  console=TRUE))

Study: rdto ~ aplic

LSD t Test for rdto 

Mean Square Error:  7.708333 

aplic,  means and individual ( 95 %) CI

       rdto       std r        LCL       UCL Min Max
1  7.666667 0.8164966 6  4.0595042 11.273829   7   9
2 14.166667 1.7224014 6 10.5595042 17.773829  12  17
3  6.500000 1.8708287 6  2.8928375 10.107162   4   9
4  4.166667 1.4719601 6  0.5595042  7.773829   2   6

Alpha: 0.05 ; DF Error: 3
Critical Value of t: 3.182446 

least Significant Difference: 5.101298 

Treatments with the same letter are not significantly different.

       rdto groups
2 14.166667      a
1  7.666667      b
3  6.500000      b
4  4.166667      b

Precaución

Si el análisis de varianza arroja que los niveles de un factor son estadísticamente similares entre sí, entonces no es necesario realizar una prueba de comparación de medias y por ende todos estos niveles pertenecen a un mismo grupo de significancia “a”.

Comparaciones de medias para las interacciones FAxFB

Para los niveles del factor A dentro del nivel B1:

  • A1 vs A2:

\(H_0: \mu_{A1} - \mu_{A2} = 0\)

\(H_1: \mu_{A1} - \mu_{A2} \neq 0\)

  • A1 vs A3:

\(H_0: \mu_{A1} - \mu_{A3} = 0\)

\(H_1: \mu_{A1} - \mu_{A3} \neq 0\)

  • A2 vs A3:

\(H_0: \mu_{A4} - \mu_{A5} = 0\)

\(H_1: \mu_{A4} - \mu_{A5} \neq 0\)

Para los niveles del factor B dentro del nivel A1:

  • B1 vs B2:

\(H_0: \mu_{B1} - \mu_{B2} = 0\)

\(H_1: \mu_{B1} - \mu_{B2} \neq 0\)

  • B1 vs B3:

\(H_0: \mu_{B1} - \mu_{B3} = 0\)

\(H_1: \mu_{B1} - \mu_{B3} \neq 0\)

  • B1 vs B4:

\(H_0: \mu_{B1} - \mu_{B4} = 0\)

\(H_1: \mu_{B1} - \mu_{B4} \neq 0\)

(…)

  • B3 vs B4:

\(H_0: \mu_{B3} - \mu_{B4} = 0\)

\(H_1: \mu_{B3} - \mu_{B4} \neq 0\)

NOTA: Repetir este proceso para cada nivel de A y cada nivel de B.

phia::testInteractions(modelo.dbca,
                       fixed = "trat",
                       across = "aplic",
                       adjustment = "none")
F Test: 
P-value adjustment method: none
          aplic1 aplic2 aplic3 Df Sum of Sq      F    Pr(>F)    
1            5.5   11.5      4  3   136.500 47.478 0.0001423 ***
2            2.5   10.5      2  3   128.500 44.696 0.0001691 ***
3            2.5    8.0      1  3    76.375 26.565 0.0007308 ***
Residuals                       6     5.750                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
phia::testInteractions(modelo.dbca,
                       fixed = "aplic",
                       across = "trat",
                       adjustment = "none")
F Test: 
P-value adjustment method: none
          trat1 trat2 Df Sum of Sq      F Pr(>F)
1           1.0  -0.5  2    2.3333 1.2174 0.3599
2           1.5   2.0  2    4.3333 2.2609 0.1854
3           1.0   0.5  2    1.0000 0.5217 0.6181
4          -2.0  -0.5  2    4.3333 2.2609 0.1854
Residuals              6    5.7500              
phia::interactionMeans(model = modelo.dbca,
                       factors = c("trat","aplic")) %>%
  plot()

Última forma más automática

filter_by_2factor_level <- function(data, factor_name1, factor_name2) {
  levels1 <- levels(data[[deparse(substitute(factor_name1))]])
  filters1 <- purrr::map(levels1, ~ filter(data, {{factor_name1}} == .x))
  names(filters1) <- levels1
  
  levels2 <- levels(data[[deparse(substitute(factor_name2))]])
  filters2 <- purrr::map(levels2, ~ filter(data, {{factor_name2}} == .x))
  names(filters2) <- levels2
  
  result <- list()
  result[[deparse(substitute(factor_name1))]] <- filters1
  result[[deparse(substitute(factor_name2))]] <- filters2
  return(result)
}
datos_filtrados <- filter_by_2factor_level(data = data,
                       factor_name1 = trat,
                       factor_name2 =  aplic)
multcomp.test_2factors <- function(object, respuesta, factor_name1, factor_name2, test, aov){
  
  # Función auxiliar para aplicar la prueba de comparaciones múltiples a un data frame
  multcomp_df <- function(df, respuesta, factor_name, test, aov){
    if (test == "LSD") {
      comp <- LSD.test(df[[respuesta]],
                       df[[factor_name]],
                       DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                       group=TRUE,
                       main = NULL,
                       console=FALSE)[[5]]
    } else if (test == "HSD") {
      comp <- HSD.test(df[[respuesta]],
                       df[[factor_name]],
                       DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                       group=TRUE,
                       main = NULL,
                       console=FALSE)[[5]]
    } else if (test == "duncan") {
      comp <- duncan.test(df[[respuesta]],
                          df[[factor_name]],
                          DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                          group=TRUE,
                          main = NULL,
                          console=FALSE)[[6]]
    } else if (test == "SNK") {
      comp <- SNK.test(df[[respuesta]],
                       df[[factor_name]],
                       DFerror = df.residual(aov), 
                       MSerror = dvmisc::get_mse(aov),
                       alpha = 0.05,
                       group=TRUE,
                       main = NULL,
                       console=FALSE)[[6]]
    } else {
      stop("Test no válido. Los tests disponibles son LSD, HSD, duncan, y SNK.")
    }
    
    return(comp %>%
             rename("y" = "df[[respuesta]]")
           )
  }
  
  # Aplicar la prueba de comparaciones múltiples a todos los data frames dentro de filters1
  comp_filters1 <- lapply(object[[1]], function(df){
    multcomp_df(df, respuesta, factor_name2, test, aov) %>%
      arrange(row.names(.)) %>%
      rownames_to_column(var = "x") %>%
      relocate(x)
  })
  
  # Aplicar la prueba de comparaciones múltiples a todos los data frames dentro de filters2
  comp_filters2 <- lapply(object[[2]], function(df){
    multcomp_df(df, respuesta, factor_name1, test, aov) %>%
      dplyr::arrange(row.names(.)) %>%
      rownames_to_column(var = "x") %>%
      relocate(x) %>%
      dplyr::mutate(groups = toupper(groups))
  })
  
  row.names(comp_filters1) <- NULL
  row.names(comp_filters2) <- NULL
  # Retornar una lista con las comparaciones múltiples para cada data frame
  result <- list()
  result[[as.name(substitute(factor_name1))]] <- comp_filters1
  result[[as.name(substitute(factor_name2))]] <- comp_filters2
  return(#list(#"Comparación de los niveles del factor B dentro de cada nivel del factor A",
         result#[[1]],
         # "Comparación de los niveles del factor A dentro de cada nivel del factor B",
         # result[[2]]
         # )
  )
}
multcomp.test_2factors(
  object = datos_filtrados,
  respuesta = "rdto",
  factor_name1 = "trat",
  factor_name2 = "aplic",
  test = "duncan",
  aov = modelo.dbca) -> result.comp
result.comp
$trat
$trat$`1`
  x    y groups
1 1  8.5      b
2 2 14.5      a
3 3  7.0      b
4 4  3.0      c

$trat$`2`
  x    y groups
1 1  7.0      b
2 2 15.0      a
3 3  6.5     bc
4 4  4.5      c

$trat$`3`
  x    y groups
1 1  7.5      b
2 2 13.0      a
3 3  6.0     bc
4 4  5.0      c


$aplic
$aplic$`1`
  x   y groups
1 1 8.5      A
2 2 7.0      A
3 3 7.5      A

$aplic$`2`
  x    y groups
1 1 14.5      A
2 2 15.0      A
3 3 13.0      A

$aplic$`3`
  x   y groups
1 1 7.0      A
2 2 6.5      A
3 3 6.0      A

$aplic$`4`
  x   y groups
1 1 3.0      A
2 2 4.5      A
3 3 5.0      A
# Convertir la lista a un data frame
df <- result.comp %>%
  reshape2::melt() %>% 
  ungroup() %>%
  dplyr::select(-variable) %>%
  relocate("Factor" = "L1",
           "Nivel" = "L2",
           x,
           "y" = "value",
           groups)
df
   Factor Nivel x    y groups
1    trat     1 1  8.5      b
2    trat     1 2 14.5      a
3    trat     1 3  7.0      b
4    trat     1 4  3.0      c
5    trat     2 1  7.0      b
6    trat     2 2 15.0      a
7    trat     2 3  6.5     bc
8    trat     2 4  4.5      c
9    trat     3 1  7.5      b
10   trat     3 2 13.0      a
11   trat     3 3  6.0     bc
12   trat     3 4  5.0      c
13  aplic     1 1  8.5      A
14  aplic     1 2  7.0      A
15  aplic     1 3  7.5      A
16  aplic     2 1 14.5      A
17  aplic     2 2 15.0      A
18  aplic     2 3 13.0      A
19  aplic     3 1  7.0      A
20  aplic     3 2  6.5      A
21  aplic     3 3  6.0      A
22  aplic     4 1  3.0      A
23  aplic     4 2  4.5      A
24  aplic     4 3  5.0      A
# función que filtra por los dos niveles especificados por el usuario y devuelve dos subconjuntos de datos
create_report <- function(df, level1, level2) {
  
  # # Convertir level1 y level2 en nombres simbólicos
  # level1 <- as.name(level1)
  # level2 <- as.name(level2)
  # 
  # filtrar por el primer nivel
  subset1 <- df %>% filter(Factor == level1) %>%
    rename(!!level2 := x,
           !!level1 := Nivel) %>%
    dplyr::select(-c(Factor))
  
  # filtrar por el segundo nivel
  subset2 <- df %>% filter(Factor == level2) %>%
    rename(!!level1 := x,
           !!level2 := Nivel) %>%
    dplyr::select(-c(Factor,y))
  
  df <- subset1 %>% 
    dplyr::left_join(subset2,
              by = c(level1, level2)) %>%
    dplyr::mutate(groups = paste0(groups.y,groups.x)) %>%
    dplyr::select(!!level1,!!level2, y, groups) #%>%
    # rename(!!level1 := x,
    #        !!level2 := Nivel)
  
  # devolver una lista con los dos subconjuntos
  return(df)
}
df2 <- create_report(df = df,
               level1 = "trat",
               level2 = "aplic") 
df2 %>% gt()
trat aplic y groups
1 1 8.5 Ab
1 2 14.5 Aa
1 3 7.0 Ab
1 4 3.0 Ac
2 1 7.0 Ab
2 2 15.0 Aa
2 3 6.5 Abc
2 4 4.5 Ac
3 1 7.5 Ab
3 2 13.0 Aa
3 3 6.0 Abc
3 4 5.0 Ac
# función que filtra por los dos niveles especificados por el usuario y devuelve dos subconjuntos de datos
create_report <- function(df, level1, level2) {
  
  # filtrar por el primer nivel
  subset1 <- df %>% filter(Factor == level1) %>%
    rename(!!level2 := x,
           !!level1 := Nivel) %>%
    dplyr::select(-c(Factor))
  
  # filtrar por el segundo nivel
  subset2 <- df %>% filter(Factor == level2) %>%
    rename(!!level1 := x,
           !!level2 := Nivel) %>%
    dplyr::select(-c(Factor,y))
  
  df <- subset1 %>% 
    dplyr::left_join(subset2,
              by = c(level1,level2)) %>%
    dplyr::mutate(y = paste0(round(y,2), " ", groups.y, groups.x)) %>%
    dplyr::select(!!level1,!!level2, y)
  
  # devolver una lista con los dos subconjuntos
  return(df)
}
df3 <- create_report(df = df,
               level1 = "trat",
               level2 = "aplic") 
df3 %>% gt()
trat aplic y
1 1 8.5 Ab
1 2 14.5 Aa
1 3 7 Ab
1 4 3 Ac
2 1 7 Ab
2 2 15 Aa
2 3 6.5 Abc
2 4 4.5 Ac
3 1 7.5 Ab
3 2 13 Aa
3 3 6 Abc
3 4 5 Ac
df3 %>% 
 pivot_wider(names_from = aplic,
             values_from = c(y), 
             names_glue = "{aplic}") %>%
  gt()
trat 1 2 3 4
1 8.5 Ab 14.5 Aa 7 Ab 3 Ac
2 7 Ab 15 Aa 6.5 Abc 4.5 Ac
3 7.5 Ab 13 Aa 6 Abc 5 Ac

DBCA en arreglo de bloques divididos con el paquete ExpDes

data %>%
with(ExpDes::strip(factor1 = trat,
              factor2 = aplic,
              block = bloque,
              resp = rdto,
              quali = c(T,T),
              mcomp = "duncan",
              fac.names = c("Tratamiento",
                            "Aplicación"),
              sigT = 0.05,
              sigF = 0.05,
              unfold = 1))
------------------------------------------------------------------------
Legend:
FACTOR 1 (Whole plot):  Tratamiento 
FACTOR 2 (strip-plot):  Aplicación 
------------------------------------------------------------------------

------------------------------------------------------------------------
Analysis of variance table
------------------------------------------------------------------------
                       DF     SS      MS      Fc Pr(>Fc)  
Block                   1   3.38   3.375  0.4286 0.57992  
Tratamiento             2   0.75   0.375  0.3333 0.75000  
Error a                 2   2.25   1.125                  
Aplicación              3 330.12 110.042 14.2757 0.02787 *
Error b                 3  23.12   7.708                  
Tratamiento*Aplicación  6  11.25   1.875  1.9565 0.21719  
Error c                 6   5.75   0.958                  
Total                  23 376.62                          
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------------------------------------
CV 1 = 13.05428 %
CV 2 = 34.17094 %
CV 3 = 12.04855 %

------------------------------------------------------------------------
Shapiro-Wilk normality test (Error b)
p-value:  0.9973946 
According to Shapiro-Wilk normality test at 5% of significance, residuals can be considered normal.
------------------------------------------------------------------------

No significant interaction: analyzing the main effects
------------------------------------------------------------------------
Tratamiento
According to F test, the means of this factor are not different.
------------------------------------------------------------------------
  Levels Means
1      1 8.250
2      2 8.250
3      3 7.875
------------------------------------------------------------------------
Aplicación
Duncan's test 
------------------------------------------------------------------------
Groups  Treatments  Means
a    2       14.16667 
 b   1       7.666667 
 b   3       6.5 
 b   4       4.166667 
------------------------------------------------------------------------